Best Known (4, 4+6, s)-Nets in Base 16
(4, 4+6, 45)-Net over F16 — Constructive and digital
Digital (4, 10, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
(4, 4+6, 65)-Net in Base 16 — Constructive
(4, 10, 65)-net in base 16, using
- 2 times m-reduction [i] based on (4, 12, 65)-net in base 16, using
- base change [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
- base change [i] based on digital (0, 8, 65)-net over F64, using
(4, 4+6, 74)-Net over F16 — Digital
Digital (4, 10, 74)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1610, 74, F16, 6) (dual of [74, 64, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(1610, 85, F16, 6) (dual of [85, 75, 7]-code), using
(4, 4+6, 1249)-Net in Base 16 — Upper bound on s
There is no (4, 10, 1250)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 101798 759376 > 1610 [i]