Best Known (33, 33+49, s)-Nets in Base 81
(33, 33+49, 370)-Net over F81 — Constructive and digital
Digital (33, 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
(33, 33+49, 576)-Net over F81 — Digital
Digital (33, 82, 576)-net over F81, using
- net from sequence [i] based on digital (33, 575)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 33 and N(F) ≥ 576, using
(33, 33+49, 338372)-Net in Base 81 — Upper bound on s
There is no (33, 82, 338373)-net in base 81, because
- 1 times m-reduction [i] would yield (33, 81, 338373)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 38664 672311 730162 804837 472453 686151 815362 461297 445275 608023 522681 123588 584304 110821 861222 182536 001448 094857 903594 521078 054811 872120 644678 056692 033157 042561 > 8181 [i]