Best Known (155−28, 155, s)-Nets in Base 4
(155−28, 155, 1223)-Net over F4 — Constructive and digital
Digital (127, 155, 1223)-net over F4, using
- 41 times duplication [i] based on digital (126, 154, 1223)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (28, 42, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 14, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 14, 65)-net over F64, using
- digital (84, 112, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 28, 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, 28, 257)-net over F256, using
- digital (28, 42, 195)-net over F4, using
- (u, u+v)-construction [i] based on
(155−28, 155, 12928)-Net over F4 — Digital
Digital (127, 155, 12928)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4155, 12928, F4, 28) (dual of [12928, 12773, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4155, 16419, F4, 28) (dual of [16419, 16264, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(4155, 16419, F4, 28) (dual of [16419, 16264, 29]-code), using
(155−28, 155, large)-Net in Base 4 — Upper bound on s
There is no (127, 155, large)-net in base 4, because
- 26 times m-reduction [i] would yield (127, 129, large)-net in base 4, but