Best Known (169, 206, s)-Nets in Base 4
(169, 206, 1539)-Net over F4 — Constructive and digital
Digital (169, 206, 1539)-net over F4, using
- t-expansion [i] based on digital (168, 206, 1539)-net over F4, using
- 4 times m-reduction [i] based on digital (168, 210, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 70, 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, 70, 513)-net over F64, using
- 4 times m-reduction [i] based on digital (168, 210, 1539)-net over F4, using
(169, 206, 15549)-Net over F4 — Digital
Digital (169, 206, 15549)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4206, 15549, F4, 37) (dual of [15549, 15343, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4206, 16442, F4, 37) (dual of [16442, 16236, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(4206, 16442, F4, 37) (dual of [16442, 16236, 38]-code), using
(169, 206, large)-Net in Base 4 — Upper bound on s
There is no (169, 206, large)-net in base 4, because
- 35 times m-reduction [i] would yield (169, 171, large)-net in base 4, but