Best Known (197, 197+28, s)-Nets in Base 2
(197, 197+28, 4682)-Net over F2 — Constructive and digital
Digital (197, 225, 4682)-net over F2, using
- net defined by OOA [i] based on linear OOA(2225, 4682, F2, 28, 28) (dual of [(4682, 28), 130871, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2225, 65548, F2, 28) (dual of [65548, 65323, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2225, 65552, F2, 28) (dual of [65552, 65327, 29]-code), using
- 1 times truncation [i] based on linear OA(2226, 65553, F2, 29) (dual of [65553, 65327, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2225, 65536, F2, 29) (dual of [65536, 65311, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2209, 65536, F2, 27) (dual of [65536, 65327, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2226, 65553, F2, 29) (dual of [65553, 65327, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2225, 65552, F2, 28) (dual of [65552, 65327, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2225, 65548, F2, 28) (dual of [65548, 65323, 29]-code), using
(197, 197+28, 10925)-Net over F2 — Digital
Digital (197, 225, 10925)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2225, 10925, F2, 6, 28) (dual of [(10925, 6), 65325, 29]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2225, 65550, F2, 28) (dual of [65550, 65325, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2225, 65552, F2, 28) (dual of [65552, 65327, 29]-code), using
- 1 times truncation [i] based on linear OA(2226, 65553, F2, 29) (dual of [65553, 65327, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2225, 65536, F2, 29) (dual of [65536, 65311, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2209, 65536, F2, 27) (dual of [65536, 65327, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2226, 65553, F2, 29) (dual of [65553, 65327, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2225, 65552, F2, 28) (dual of [65552, 65327, 29]-code), using
- OOA 6-folding [i] based on linear OA(2225, 65550, F2, 28) (dual of [65550, 65325, 29]-code), using
(197, 197+28, 416311)-Net in Base 2 — Upper bound on s
There is no (197, 225, 416312)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 53 920764 666664 493977 504087 517854 052884 630584 940858 061443 467689 492594 > 2225 [i]