Best Known (23, 27, s)-Nets in Base 2
(23, 27, 8193)-Net over F2 — Constructive and digital
Digital (23, 27, 8193)-net over F2, using
(23, 27, 8206)-Net over F2 — Digital
Digital (23, 27, 8206)-net over F2, using
- net defined by OOA [i] based on linear OOA(227, 8206, F2, 4, 4) (dual of [(8206, 4), 32797, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(227, 8206, F2, 3, 4) (dual of [(8206, 3), 24591, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(227, 8206, F2, 4) (dual of [8206, 8179, 5]-code), using
- 1 times truncation [i] based on linear OA(228, 8207, F2, 5) (dual of [8207, 8179, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(227, 8192, F2, 5) (dual of [8192, 8165, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(214, 8192, F2, 3) (dual of [8192, 8178, 4]-code or 8192-cap in PG(13,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(214, 15, F2, 13) (dual of [15, 1, 14]-code), using
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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 X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- 1 times truncation [i] based on linear OA(228, 8207, F2, 5) (dual of [8207, 8179, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(227, 8206, F2, 4) (dual of [8206, 8179, 5]-code), using
- appending kth column [i] based on linear OOA(227, 8206, F2, 3, 4) (dual of [(8206, 3), 24591, 5]-NRT-code), using
(23, 27, 16381)-Net in Base 2 — Upper bound on s
There is no (23, 27, 16382)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 134 225918 > 227 [i]