Best Known (17, 68, s)-Nets in Base 16
(17, 68, 65)-Net over F16 — Constructive and digital
Digital (17, 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
(17, 68, 112)-Net over F16 — Digital
Digital (17, 68, 112)-net over F16, using
- net from sequence [i] based on digital (17, 111)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 17 and N(F) ≥ 112, using
(17, 68, 1130)-Net in Base 16 — Upper bound on s
There is no (17, 68, 1131)-net in base 16, because
- 1 times m-reduction [i] would yield (17, 67, 1131)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 476 673253 427239 774197 199651 345275 136019 031217 769257 235405 149143 019816 290898 447876 > 1667 [i]