Best Known (59−49, 59, s)-Nets in Base 81
(59−49, 59, 172)-Net over F81 — Constructive and digital
Digital (10, 59, 172)-net over F81, using
- t-expansion [i] based on digital (7, 59, 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
(59−49, 59, 244)-Net over F81 — Digital
Digital (10, 59, 244)-net over F81, using
- t-expansion [i] based on digital (9, 59, 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
(59−49, 59, 5005)-Net in Base 81 — Upper bound on s
There is no (10, 59, 5006)-net in base 81, because
- 1 times m-reduction [i] would yield (10, 58, 5006)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 494 040995 035084 264790 582034 632887 666589 743068 880884 149018 697035 601141 288629 303365 575738 621522 998385 426350 193921 > 8158 [i]