Best Known (22, 22+6, s)-Nets in Base 2
(22, 22+6, 510)-Net over F2 — Constructive and digital
Digital (22, 28, 510)-net over F2, using
- 1 times m-reduction [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
(22, 22+6, 511)-Net over F2 — Digital
Digital (22, 28, 511)-net over F2, using
- net defined by OOA [i] based on linear OOA(228, 511, F2, 6, 6) (dual of [(511, 6), 3038, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(228, 511, F2, 5, 6) (dual of [(511, 5), 2527, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(228, 511, F2, 2, 6) (dual of [(511, 2), 994, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(228, 511, F2, 5, 6) (dual of [(511, 5), 2527, 7]-NRT-code), using
(22, 22+6, 1168)-Net in Base 2 — Upper bound on s
There is no (22, 28, 1169)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 268 990408 > 228 [i]