Best Known (9, 9+8, s)-Nets in Base 4
(9, 9+8, 34)-Net over F4 — Constructive and digital
Digital (9, 17, 34)-net over F4, using
- 1 times m-reduction [i] based on digital (9, 18, 34)-net over F4, using
- trace code for nets [i] based on digital (0, 9, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- trace code for nets [i] based on digital (0, 9, 17)-net over F16, using
(9, 9+8, 37)-Net over F4 — Digital
Digital (9, 17, 37)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(417, 37, F4, 8) (dual of [37, 20, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(417, 39, F4, 8) (dual of [39, 22, 9]-code), using
- 5 times truncation [i] based on linear OA(422, 44, F4, 13) (dual of [44, 22, 14]-code), using
- extended quadratic residue code Qe(44,4) [i]
- 5 times truncation [i] based on linear OA(422, 44, F4, 13) (dual of [44, 22, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(417, 39, F4, 8) (dual of [39, 22, 9]-code), using
(9, 9+8, 264)-Net in Base 4 — Upper bound on s
There is no (9, 17, 265)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 17364 122086 > 417 [i]