Best Known (24, 68, s)-Nets in Base 16
(24, 68, 65)-Net over F16 — Constructive and digital
Digital (24, 68, 65)-net over F16, using
- t-expansion [i] based on digital (6, 68, 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
(24, 68, 104)-Net in Base 16 — Constructive
(24, 68, 104)-net in base 16, using
- 7 times m-reduction [i] based on (24, 75, 104)-net in base 16, using
- base change [i] based on digital (9, 60, 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, 60, 104)-net over F32, using
(24, 68, 129)-Net over F16 — Digital
Digital (24, 68, 129)-net over F16, using
- t-expansion [i] based on digital (19, 68, 129)-net over F16, using
- net from sequence [i] based on digital (19, 128)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 19 and N(F) ≥ 129, using
- net from sequence [i] based on digital (19, 128)-sequence over F16, using
(24, 68, 3169)-Net in Base 16 — Upper bound on s
There is no (24, 68, 3170)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 7629 751941 847788 648257 807099 397598 400824 427568 044949 974060 418242 118626 226540 108976 > 1668 [i]