Best Known (230−41, 230, s)-Nets in Base 4
(230−41, 230, 1553)-Net over F4 — Constructive and digital
Digital (189, 230, 1553)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 23, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (166, 207, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 69, 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, 69, 513)-net over F64, using
- digital (3, 23, 14)-net over F4, using
(230−41, 230, 16450)-Net over F4 — Digital
Digital (189, 230, 16450)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4230, 16450, F4, 41) (dual of [16450, 16220, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(30) [i] based on
- 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(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(419, 66, F4, 9) (dual of [66, 47, 10]-code), using
- construction X applied to Ce(40) ⊂ Ce(30) [i] based on
(230−41, 230, large)-Net in Base 4 — Upper bound on s
There is no (189, 230, large)-net in base 4, because
- 39 times m-reduction [i] would yield (189, 191, large)-net in base 4, but