Best Known (123, 150, s)-Nets in Base 4
(123, 150, 1268)-Net over F4 — Constructive and digital
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
(123, 150, 13126)-Net over F4 — Digital
Digital (123, 150, 13126)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4150, 13126, F4, 27) (dual of [13126, 12976, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4150, 16409, F4, 27) (dual of [16409, 16259, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [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(4113, 16385, F4, 21) (dual of [16385, 16272, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(49, 24, F4, 5) (dual of [24, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 36, F4, 5) (dual of [36, 27, 6]-code), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4150, 16409, F4, 27) (dual of [16409, 16259, 28]-code), using
(123, 150, large)-Net in Base 4 — Upper bound on s
There is no (123, 150, large)-net in base 4, because
- 25 times m-reduction [i] would yield (123, 125, large)-net in base 4, but