Best Known (23, 23+7, s)-Nets in Base 2
(23, 23+7, 510)-Net over F2 — Constructive and digital
Digital (23, 30, 510)-net over F2, using
- 21 times duplication [i] based on digital (22, 29, 510)-net over F2, using
- net defined by OOA [i] based on linear OOA(229, 510, F2, 7, 7) (dual of [(510, 7), 3541, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(229, 511, F2, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(229, 510, F2, 7, 7) (dual of [(510, 7), 3541, 8]-NRT-code), using
(23, 23+7, 511)-Net over F2 — Digital
Digital (23, 30, 511)-net over F2, using
- 21 times duplication [i] based on digital (22, 29, 511)-net over F2, using
- net defined by OOA [i] based on linear OOA(229, 511, F2, 7, 7) (dual of [(511, 7), 3548, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(229, 511, F2, 6, 7) (dual of [(511, 6), 3037, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(229, 511, F2, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(229, 511, F2, 6, 7) (dual of [(511, 6), 3037, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(229, 511, F2, 7, 7) (dual of [(511, 7), 3548, 8]-NRT-code), using
(23, 23+7, 1472)-Net in Base 2 — Upper bound on s
There is no (23, 30, 1473)-net in base 2, because
- 1 times m-reduction [i] would yield (23, 29, 1473)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 537 015048 > 229 [i]