Best Known (64−54, 64, s)-Nets in Base 81
(64−54, 64, 172)-Net over F81 — Constructive and digital
Digital (10, 64, 172)-net over F81, using
- t-expansion [i] based on digital (7, 64, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(64−54, 64, 244)-Net over F81 — Digital
Digital (10, 64, 244)-net over F81, using
- t-expansion [i] based on digital (9, 64, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
(64−54, 64, 4548)-Net in Base 81 — Upper bound on s
There is no (10, 64, 4549)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 139 472093 337304 435467 949463 096227 666267 522762 808231 682842 744647 117665 233547 786672 223157 354811 605297 876230 980997 796107 265841 > 8164 [i]