Best Known (51−43, 51, s)-Nets in Base 81
(51−43, 51, 172)-Net over F81 — Constructive and digital
Digital (8, 51, 172)-net over F81, using
- t-expansion [i] based on digital (7, 51, 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
(51−43, 51, 226)-Net over F81 — Digital
Digital (8, 51, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
(51−43, 51, 3786)-Net in Base 81 — Upper bound on s
There is no (8, 51, 3787)-net in base 81, because
- 1 times m-reduction [i] would yield (8, 50, 3787)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 266327 228531 710029 419872 597875 684873 713901 998035 291625 882273 116482 332314 897697 183351 157478 234161 > 8150 [i]