Best Known (194−35, 194, s)-Nets in Base 4
(194−35, 194, 1539)-Net over F4 — Constructive and digital
Digital (159, 194, 1539)-net over F4, using
- t-expansion [i] based on digital (158, 194, 1539)-net over F4, using
- 1 times m-reduction [i] based on digital (158, 195, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 65, 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, 65, 513)-net over F64, using
- 1 times m-reduction [i] based on digital (158, 195, 1539)-net over F4, using
(194−35, 194, 14541)-Net over F4 — Digital
Digital (159, 194, 14541)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4194, 14541, F4, 35) (dual of [14541, 14347, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4194, 16430, F4, 35) (dual of [16430, 16236, 36]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4193, 16429, F4, 35) (dual of [16429, 16236, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(4183, 16384, F4, 35) (dual of [16384, 16201, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4193, 16429, F4, 35) (dual of [16429, 16236, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4194, 16430, F4, 35) (dual of [16430, 16236, 36]-code), using
(194−35, 194, large)-Net in Base 4 — Upper bound on s
There is no (159, 194, large)-net in base 4, because
- 33 times m-reduction [i] would yield (159, 161, large)-net in base 4, but