Best Known (175, 175+26, s)-Nets in Base 2
(175, 175+26, 2523)-Net over F2 — Constructive and digital
Digital (175, 201, 2523)-net over F2, using
- net defined by OOA [i] based on linear OOA(2201, 2523, F2, 26, 26) (dual of [(2523, 26), 65397, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2201, 32799, F2, 26) (dual of [32799, 32598, 27]-code), using
- 1 times truncation [i] based on linear OA(2202, 32800, F2, 27) (dual of [32800, 32598, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2166, 32768, F2, 23) (dual of [32768, 32602, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2202, 32800, F2, 27) (dual of [32800, 32598, 28]-code), using
- OA 13-folding and stacking [i] based on linear OA(2201, 32799, F2, 26) (dual of [32799, 32598, 27]-code), using
(175, 175+26, 6559)-Net over F2 — Digital
Digital (175, 201, 6559)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2201, 6559, F2, 5, 26) (dual of [(6559, 5), 32594, 27]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2201, 32795, F2, 26) (dual of [32795, 32594, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2201, 32799, F2, 26) (dual of [32799, 32598, 27]-code), using
- 1 times truncation [i] based on linear OA(2202, 32800, F2, 27) (dual of [32800, 32598, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2166, 32768, F2, 23) (dual of [32768, 32602, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2202, 32800, F2, 27) (dual of [32800, 32598, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2201, 32799, F2, 26) (dual of [32799, 32598, 27]-code), using
- OOA 5-folding [i] based on linear OA(2201, 32795, F2, 26) (dual of [32795, 32594, 27]-code), using
(175, 175+26, 255717)-Net in Base 2 — Upper bound on s
There is no (175, 201, 255718)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3 213927 167539 210017 681841 957644 339582 266240 289839 313821 091572 > 2201 [i]