Best Known (22, 30, s)-Nets in Base 4
(22, 30, 514)-Net over F4 — Constructive and digital
Digital (22, 30, 514)-net over F4, using
- trace code for nets [i] based on digital (7, 15, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(7,256) in PG(14,16)) for nets [i] based on digital (0, 8, 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
- base reduction for projective spaces (embedding PG(7,256) in PG(14,16)) for nets [i] based on digital (0, 8, 257)-net over F256, using
(22, 30, 807)-Net over F4 — Digital
Digital (22, 30, 807)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(430, 807, F4, 8) (dual of [807, 777, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(430, 1023, F4, 8) (dual of [1023, 993, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(430, 1023, F4, 8) (dual of [1023, 993, 9]-code), using
(22, 30, 24173)-Net in Base 4 — Upper bound on s
There is no (22, 30, 24174)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 153111 846515 487939 > 430 [i]