Best Known (126, 153, s)-Nets in Base 4
(126, 153, 1268)-Net over F4 — Constructive and digital
Digital (126, 153, 1268)-net over F4, using
- 43 times duplication [i] based on digital (123, 150, 1268)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (29, 42, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 14, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 14, 80)-net over F64, using
- digital (81, 108, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 27, 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, 27, 257)-net over F256, using
- digital (29, 42, 240)-net over F4, using
- (u, u+v)-construction [i] based on
(126, 153, 15505)-Net over F4 — Digital
Digital (126, 153, 15505)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4153, 15505, F4, 27) (dual of [15505, 15352, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4153, 16398, F4, 27) (dual of [16398, 16245, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([1,13]) [i] based on
- 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(4140, 16385, F4, 14) (dual of [16385, 16245, 15]-code), using the narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [1,13], and minimum distance d ≥ |{−13,−11,−9,…,13}|+1 = 15 (BCH-bound) [i]
- linear OA(412, 13, F4, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,4)), using
- dual of repetition code with length 13 [i]
- construction X applied to C([0,13]) ⊂ C([1,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4153, 16398, F4, 27) (dual of [16398, 16245, 28]-code), using
(126, 153, large)-Net in Base 4 — Upper bound on s
There is no (126, 153, large)-net in base 4, because
- 25 times m-reduction [i] would yield (126, 128, large)-net in base 4, but