Best Known (13, 13+22, s)-Nets in Base 16
(13, 13+22, 65)-Net over F16 — Constructive and digital
Digital (13, 35, 65)-net over F16, using
- t-expansion [i] based on digital (6, 35, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(13, 13+22, 80)-Net in Base 16 — Constructive
(13, 35, 80)-net in base 16, using
- 1 times m-reduction [i] based on (13, 36, 80)-net in base 16, using
- base change [i] based on digital (1, 24, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- base change [i] based on digital (1, 24, 80)-net over F64, using
(13, 13+22, 97)-Net over F16 — Digital
Digital (13, 35, 97)-net over F16, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 13 and N(F) ≥ 97, using
(13, 13+22, 2213)-Net in Base 16 — Upper bound on s
There is no (13, 35, 2214)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 396845 391841 887101 422109 185730 607847 020936 > 1635 [i]