Best Known (191−30, 191, s)-Nets in Base 2
(191−30, 191, 490)-Net over F2 — Constructive and digital
Digital (161, 191, 490)-net over F2, using
- 21 times duplication [i] based on digital (160, 190, 490)-net over F2, using
- t-expansion [i] based on digital (159, 190, 490)-net over F2, using
- trace code for nets [i] based on digital (7, 38, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- trace code for nets [i] based on digital (7, 38, 98)-net over F32, using
- t-expansion [i] based on digital (159, 190, 490)-net over F2, using
(191−30, 191, 1376)-Net over F2 — Digital
Digital (161, 191, 1376)-net over F2, using
- 22 times duplication [i] based on digital (159, 189, 1376)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2189, 1376, F2, 3, 30) (dual of [(1376, 3), 3939, 31]-NRT-code), using
- strength reduction [i] based on linear OOA(2189, 1376, F2, 3, 31) (dual of [(1376, 3), 3939, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2189, 4128, F2, 31) (dual of [4128, 3939, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2187, 4126, F2, 31) (dual of [4126, 3939, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on 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(30) ⊂ Ce(26) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2187, 4126, F2, 31) (dual of [4126, 3939, 32]-code), using
- OOA 3-folding [i] based on linear OA(2189, 4128, F2, 31) (dual of [4128, 3939, 32]-code), using
- strength reduction [i] based on linear OOA(2189, 1376, F2, 3, 31) (dual of [(1376, 3), 3939, 32]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2189, 1376, F2, 3, 30) (dual of [(1376, 3), 3939, 31]-NRT-code), using
(191−30, 191, 43718)-Net in Base 2 — Upper bound on s
There is no (161, 191, 43719)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3139 281466 760369 454095 754379 879313 316596 685768 515277 926608 > 2191 [i]