Best Known (246−46, 246, s)-Nets in Base 4
(246−46, 246, 1548)-Net over F4 — Constructive and digital
Digital (200, 246, 1548)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 24, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (176, 222, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 74, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 74, 513)-net over F64, using
- digital (1, 24, 9)-net over F4, using
(246−46, 246, 12912)-Net over F4 — Digital
Digital (200, 246, 12912)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4246, 12912, F4, 46) (dual of [12912, 12666, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(4246, 16419, F4, 46) (dual of [16419, 16173, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(40) [i] based on
- linear OA(4239, 16384, F4, 46) (dual of [16384, 16145, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(45) ⊂ Ce(40) [i] based on
- discarding factors / shortening the dual code based on linear OA(4246, 16419, F4, 46) (dual of [16419, 16173, 47]-code), using
(246−46, 246, large)-Net in Base 4 — Upper bound on s
There is no (200, 246, large)-net in base 4, because
- 44 times m-reduction [i] would yield (200, 202, large)-net in base 4, but