Best Known (31, 105, s)-Nets in Base 16
(31, 105, 65)-Net over F16 — Constructive and digital
Digital (31, 105, 65)-net over F16, using
- t-expansion [i] based on digital (6, 105, 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
(31, 105, 104)-Net in Base 16 — Constructive
(31, 105, 104)-net in base 16, using
- 5 times m-reduction [i] based on (31, 110, 104)-net in base 16, using
- base change [i] based on digital (9, 88, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 88, 104)-net over F32, using
(31, 105, 168)-Net over F16 — Digital
Digital (31, 105, 168)-net over F16, using
- net from sequence [i] based on digital (31, 167)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 31 and N(F) ≥ 168, using
(31, 105, 2531)-Net in Base 16 — Upper bound on s
There is no (31, 105, 2532)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 715850 397591 132290 049076 763585 598766 763854 953980 047616 899365 935413 092648 669005 991113 328505 858913 549478 211780 157406 907945 217936 > 16105 [i]