Best Known (143, 170, s)-Nets in Base 2
(143, 170, 630)-Net over F2 — Constructive and digital
Digital (143, 170, 630)-net over F2, using
- net defined by OOA [i] based on linear OOA(2170, 630, F2, 27, 27) (dual of [(630, 27), 16840, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2170, 8191, F2, 27) (dual of [8191, 8021, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2170, 8191, F2, 27) (dual of [8191, 8021, 28]-code), using
(143, 170, 1660)-Net over F2 — Digital
Digital (143, 170, 1660)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2170, 1660, F2, 4, 27) (dual of [(1660, 4), 6470, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2170, 2048, F2, 4, 27) (dual of [(2048, 4), 8022, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- OOA 4-folding [i] based on linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(2170, 2048, F2, 4, 27) (dual of [(2048, 4), 8022, 28]-NRT-code), using
(143, 170, 46410)-Net in Base 2 — Upper bound on s
There is no (143, 170, 46411)-net in base 2, because
- 1 times m-reduction [i] would yield (143, 169, 46411)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 748 345487 939496 423680 015237 285871 935963 200435 151024 > 2169 [i]