Best Known (195, 195+22, s)-Nets in Base 2
(195, 195+22, 47666)-Net over F2 — Constructive and digital
Digital (195, 217, 47666)-net over F2, using
- t-expansion [i] based on digital (194, 217, 47666)-net over F2, using
- net defined by OOA [i] based on linear OOA(2217, 47666, F2, 23, 23) (dual of [(47666, 23), 1096101, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2217, 524327, F2, 23) (dual of [524327, 524110, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2217, 524333, F2, 23) (dual of [524333, 524116, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2172, 524288, F2, 19) (dual of [524288, 524116, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(2217, 524333, F2, 23) (dual of [524333, 524116, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2217, 524327, F2, 23) (dual of [524327, 524110, 24]-code), using
- net defined by OOA [i] based on linear OOA(2217, 47666, F2, 23, 23) (dual of [(47666, 23), 1096101, 24]-NRT-code), using
(195, 195+22, 87388)-Net over F2 — Digital
Digital (195, 217, 87388)-net over F2, using
- 21 times duplication [i] based on digital (194, 216, 87388)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2216, 87388, F2, 6, 22) (dual of [(87388, 6), 524112, 23]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2216, 524328, F2, 22) (dual of [524328, 524112, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2216, 524332, F2, 22) (dual of [524332, 524116, 23]-code), using
- 1 times truncation [i] based on linear OA(2217, 524333, F2, 23) (dual of [524333, 524116, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2172, 524288, F2, 19) (dual of [524288, 524116, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2217, 524333, F2, 23) (dual of [524333, 524116, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2216, 524332, F2, 22) (dual of [524332, 524116, 23]-code), using
- OOA 6-folding [i] based on linear OA(2216, 524328, F2, 22) (dual of [524328, 524112, 23]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2216, 87388, F2, 6, 22) (dual of [(87388, 6), 524112, 23]-NRT-code), using
(195, 195+22, 4261017)-Net in Base 2 — Upper bound on s
There is no (195, 217, 4261018)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 210624 689138 913107 572467 948995 538357 851971 976256 246662 570708 412036 > 2217 [i]