  Type Ia supernovae are thought to occur as a white dwarf made of carbon and
oxygen accretes sufficient mass to trigger a thermonuclear explosion$^{1}$. The
accretion could occur slowly from an unevolved (main-sequence) or evolved
(subgiant or giant) star$^{2,3}$, that being dubbed the single-degenerate
channel, or rapidly as it breaks up a smaller orbiting white dwarf (the double-
degenerate channel)$^{3,4}$. Obviously, a companion will survive the explosion
only in the single-degenerate channel$^{5}$. Both channels might contribute to
the production of type Ia supernovae$^{6,7}$ but their relative proportions
still remain a fundamental puzzle in astronomy. Previous searches for remnant
companions have revealed one possible case for SN 1572$^{8,9}$, though that has
been criticized$^{10}$. More recently, observations have restricted surviving
companions to be small, main-sequence stars$^{11,12,13}$, ruling out giant
companions, though still allowing the single-degenerate channel. Here we report
the result of a search for surviving companions to the progenitor of SN
1006$^{14}$. None of the stars within 4' of the apparent site of the explosion
is associated with the supernova remnant, so we can firmly exclude all giant
and subgiant companions to the progenitor. Combined with the previous results,
less than 20 per cent of type Iae occur through the single degenerate channel.
