Best Known (31, 82, s)-Nets in Base 81
(31, 82, 370)-Net over F81 — Constructive and digital
Digital (31, 82, 370)-net over F81, using
- t-expansion [i] based on digital (16, 82, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(31, 82, 551)-Net over F81 — Digital
Digital (31, 82, 551)-net over F81, using
- t-expansion [i] based on digital (30, 82, 551)-net over F81, using
- net from sequence [i] based on digital (30, 550)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 30 and N(F) ≥ 551, using
- net from sequence [i] based on digital (30, 550)-sequence over F81, using
(31, 82, 194088)-Net in Base 81 — Upper bound on s
There is no (31, 82, 194089)-net in base 81, because
- 1 times m-reduction [i] would yield (31, 81, 194089)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 38664 801871 749453 105353 150174 866893 172781 794145 643575 163372 424155 298497 985262 746553 571529 706483 114176 322940 611846 960389 407521 647504 843516 752862 340365 778001 > 8181 [i]