Best Known (154, 182, s)-Nets in Base 2
(154, 182, 585)-Net over F2 — Constructive and digital
Digital (154, 182, 585)-net over F2, using
- net defined by OOA [i] based on linear OOA(2182, 585, F2, 28, 28) (dual of [(585, 28), 16198, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2182, 8190, F2, 28) (dual of [8190, 8008, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2182, 8192, F2, 28) (dual of [8192, 8010, 29]-code), using
- 1 times truncation [i] based on linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2182, 8192, F2, 28) (dual of [8192, 8010, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2182, 8190, F2, 28) (dual of [8190, 8008, 29]-code), using
(154, 182, 1981)-Net over F2 — Digital
Digital (154, 182, 1981)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2182, 1981, F2, 4, 28) (dual of [(1981, 4), 7742, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2182, 2048, F2, 4, 28) (dual of [(2048, 4), 8010, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2182, 8192, F2, 28) (dual of [8192, 8010, 29]-code), using
- 1 times truncation [i] based on linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using
- OOA 4-folding [i] based on linear OA(2182, 8192, F2, 28) (dual of [8192, 8010, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(2182, 2048, F2, 4, 28) (dual of [(2048, 4), 8010, 29]-NRT-code), using
(154, 182, 49507)-Net in Base 2 — Upper bound on s
There is no (154, 182, 49508)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 131456 213979 328084 603601 442923 849674 506758 316472 054392 > 2182 [i]