Best Known (40−11, 40, s)-Nets in Base 2
(40−11, 40, 60)-Net over F2 — Constructive and digital
Digital (29, 40, 60)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (7, 12, 36)-net over F2, using
- digital (17, 28, 30)-net over F2, using
- 2 times m-reduction [i] based on digital (17, 30, 30)-net over F2, using
(40−11, 40, 91)-Net over F2 — Digital
Digital (29, 40, 91)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(240, 91, F2, 2, 11) (dual of [(91, 2), 142, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(240, 96, F2, 2, 11) (dual of [(96, 2), 152, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(240, 192, F2, 11) (dual of [192, 152, 12]-code), using
- adding a parity check bit [i] based on linear OA(239, 191, F2, 10) (dual of [191, 152, 11]-code), using
- a “X†code from Brouwer’s database [i]
- adding a parity check bit [i] based on linear OA(239, 191, F2, 10) (dual of [191, 152, 11]-code), using
- OOA 2-folding [i] based on linear OA(240, 192, F2, 11) (dual of [192, 152, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(240, 96, F2, 2, 11) (dual of [(96, 2), 152, 12]-NRT-code), using
(40−11, 40, 573)-Net in Base 2 — Upper bound on s
There is no (29, 40, 574)-net in base 2, because
- 1 times m-reduction [i] would yield (29, 39, 574)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 551524 708561 > 239 [i]