Best Known (149, 149+33, s)-Nets in Base 4
(149, 149+33, 1223)-Net over F4 — Constructive and digital
Digital (149, 182, 1223)-net over F4, using
- 42 times duplication [i] based on digital (147, 180, 1223)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (32, 48, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 16, 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, 16, 65)-net over F64, using
- digital (99, 132, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 33, 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, 33, 257)-net over F256, using
- digital (32, 48, 195)-net over F4, using
- (u, u+v)-construction [i] based on
(149, 149+33, 13532)-Net over F4 — Digital
Digital (149, 182, 13532)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4182, 13532, F4, 33) (dual of [13532, 13350, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4182, 16432, F4, 33) (dual of [16432, 16250, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(413, 48, F4, 6) (dual of [48, 35, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4182, 16432, F4, 33) (dual of [16432, 16250, 34]-code), using
(149, 149+33, large)-Net in Base 4 — Upper bound on s
There is no (149, 182, large)-net in base 4, because
- 31 times m-reduction [i] would yield (149, 151, large)-net in base 4, but