Best Known (175, 197, s)-Nets in Base 2
(175, 197, 11919)-Net over F2 — Constructive and digital
Digital (175, 197, 11919)-net over F2, using
- 22 times duplication [i] based on digital (173, 195, 11919)-net over F2, using
- t-expansion [i] based on digital (172, 195, 11919)-net over F2, using
- net defined by OOA [i] based on linear OOA(2195, 11919, F2, 23, 23) (dual of [(11919, 23), 273942, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2195, 131110, F2, 23) (dual of [131110, 130915, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2195, 131113, F2, 23) (dual of [131113, 130918, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2188, 131072, F2, 23) (dual of [131072, 130884, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2154, 131072, F2, 19) (dual of [131072, 130918, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 41, F2, 3) (dual of [41, 34, 4]-code or 41-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(2195, 131113, F2, 23) (dual of [131113, 130918, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2195, 131110, F2, 23) (dual of [131110, 130915, 24]-code), using
- net defined by OOA [i] based on linear OOA(2195, 11919, F2, 23, 23) (dual of [(11919, 23), 273942, 24]-NRT-code), using
- t-expansion [i] based on digital (172, 195, 11919)-net over F2, using
(175, 197, 26223)-Net over F2 — Digital
Digital (175, 197, 26223)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2197, 26223, F2, 5, 22) (dual of [(26223, 5), 130918, 23]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2197, 131115, F2, 22) (dual of [131115, 130918, 23]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2194, 131112, F2, 22) (dual of [131112, 130918, 23]-code), using
- 1 times truncation [i] based on linear OA(2195, 131113, F2, 23) (dual of [131113, 130918, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2188, 131072, F2, 23) (dual of [131072, 130884, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2154, 131072, F2, 19) (dual of [131072, 130918, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 41, F2, 3) (dual of [41, 34, 4]-code or 41-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(2195, 131113, F2, 23) (dual of [131113, 130918, 24]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2194, 131112, F2, 22) (dual of [131112, 130918, 23]-code), using
- OOA 5-folding [i] based on linear OA(2197, 131115, F2, 22) (dual of [131115, 130918, 23]-code), using
(175, 197, 1208320)-Net in Base 2 — Upper bound on s
There is no (175, 197, 1208321)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 200869 082597 307688 700888 735135 146280 205302 137144 754856 056832 > 2197 [i]