Best Known (30−6, 30, s)-Nets in Base 2
(30−6, 30, 510)-Net over F2 — Constructive and digital
Digital (24, 30, 510)-net over F2, using
- 21 times duplication [i] based on digital (23, 29, 510)-net over F2, using
- net defined by OOA [i] based on linear OOA(229, 510, F2, 6, 6) (dual of [(510, 6), 3031, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(229, 511, F2, 3, 6) (dual of [(511, 3), 1504, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(229, 511, F2, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(229, 511, F2, 3, 6) (dual of [(511, 3), 1504, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(229, 510, F2, 6, 6) (dual of [(510, 6), 3031, 7]-NRT-code), using
(30−6, 30, 512)-Net over F2 — Digital
Digital (24, 30, 512)-net over F2, using
- net defined by OOA [i] based on linear OOA(230, 512, F2, 6, 6) (dual of [(512, 6), 3042, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(230, 512, F2, 5, 6) (dual of [(512, 5), 2530, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(230, 512, F2, 2, 6) (dual of [(512, 2), 994, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(228, 511, F2, 2, 6) (dual of [(511, 2), 994, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(230, 512, F2, 2, 6) (dual of [(512, 2), 994, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(230, 512, F2, 5, 6) (dual of [(512, 5), 2530, 7]-NRT-code), using
(30−6, 30, 1856)-Net in Base 2 — Upper bound on s
There is no (24, 30, 1857)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1074 200840 > 230 [i]