Best Known (32, 69, s)-Nets in Base 81
(32, 69, 370)-Net over F81 — Constructive and digital
Digital (32, 69, 370)-net over F81, using
- t-expansion [i] based on digital (16, 69, 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
(32, 69, 830)-Net over F81 — Digital
Digital (32, 69, 830)-net over F81, using
(32, 69, 1530628)-Net in Base 81 — Upper bound on s
There is no (32, 69, 1530629)-net in base 81, because
- 1 times m-reduction [i] would yield (32, 68, 1530629)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 5983 870409 503460 127235 957142 494388 509010 365256 260337 712157 481423 348323 483015 663003 776471 001187 484785 361064 542073 398779 638500 137761 > 8168 [i]