Best Known (146, 146+33, s)-Nets in Base 4
(146, 146+33, 1158)-Net over F4 — Constructive and digital
Digital (146, 179, 1158)-net over F4, using
- 43 times duplication [i] based on digital (143, 176, 1158)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (28, 44, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 22, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 22, 65)-net over F16, 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 (28, 44, 130)-net over F4, using
- (u, u+v)-construction [i] based on
(146, 146+33, 11830)-Net over F4 — Digital
Digital (146, 179, 11830)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4179, 11830, F4, 33) (dual of [11830, 11651, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4179, 16423, F4, 33) (dual of [16423, 16244, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4141, 16385, F4, 27) (dual of [16385, 16244, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(410, 38, F4, 5) (dual of [38, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4179, 16423, F4, 33) (dual of [16423, 16244, 34]-code), using
(146, 146+33, large)-Net in Base 4 — Upper bound on s
There is no (146, 179, large)-net in base 4, because
- 31 times m-reduction [i] would yield (146, 148, large)-net in base 4, but