Best Known (71−64, 71, s)-Nets in Base 81
(71−64, 71, 172)-Net over F81 — Constructive and digital
Digital (7, 71, 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
(71−64, 71, 190)-Net over F81 — Digital
Digital (7, 71, 190)-net over F81, using
- t-expansion [i] based on digital (6, 71, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(71−64, 71, 2727)-Net in Base 81 — Upper bound on s
There is no (7, 71, 2728)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3209 242698 630421 530805 786739 375603 844290 191360 432585 382960 076948 612898 065709 578070 570853 422091 398424 139663 285405 715171 149639 273789 870081 > 8171 [i]