Best Known (33, 33+39, s)-Nets in Base 81
(33, 33+39, 370)-Net over F81 — Constructive and digital
Digital (33, 72, 370)-net over F81, using
- t-expansion [i] based on digital (16, 72, 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+39, 795)-Net over F81 — Digital
Digital (33, 72, 795)-net over F81, using
(33, 33+39, 1342238)-Net in Base 81 — Upper bound on s
There is no (33, 72, 1342239)-net in base 81, because
- 1 times m-reduction [i] would yield (33, 71, 1342239)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3180 087988 796528 704493 378144 517882 477773 044885 168235 213177 003651 250650 939500 587384 907022 589489 429980 499814 464459 462576 106527 959176 075281 > 8171 [i]