Best Known (128, 158, s)-Nets in Base 4
(128, 158, 1118)-Net over F4 — Constructive and digital
Digital (128, 158, 1118)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (23, 38, 90)-net over F4, using
- trace code for nets [i] based on digital (4, 19, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- trace code for nets [i] based on digital (4, 19, 45)-net over F16, using
- digital (90, 120, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 30, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 30, 257)-net over F256, using
- digital (23, 38, 90)-net over F4, using
(128, 158, 8926)-Net over F4 — Digital
Digital (128, 158, 8926)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4158, 8926, F4, 30) (dual of [8926, 8768, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4158, 16401, F4, 30) (dual of [16401, 16243, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(43, 17, F4, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(4158, 16401, F4, 30) (dual of [16401, 16243, 31]-code), using
(128, 158, 4702652)-Net in Base 4 — Upper bound on s
There is no (128, 158, 4702653)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 133499 563291 794274 105354 833423 611931 038405 640487 300006 747402 390532 680339 702036 125616 122481 578064 > 4158 [i]