Best Known (16, 24, s)-Nets in Base 4
(16, 24, 195)-Net over F4 — Constructive and digital
Digital (16, 24, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 8, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
(16, 24, 199)-Net over F4 — Digital
Digital (16, 24, 199)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(424, 199, F4, 8) (dual of [199, 175, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(424, 255, F4, 8) (dual of [255, 231, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(424, 255, F4, 8) (dual of [255, 231, 9]-code), using
(16, 24, 3019)-Net in Base 4 — Upper bound on s
There is no (16, 24, 3020)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 281 792845 180906 > 424 [i]