Best Known (3, 3+15, s)-Nets in Base 81
(3, 3+15, 116)-Net over F81 — Constructive and digital
Digital (3, 18, 116)-net over F81, using
- t-expansion [i] based on digital (2, 18, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
(3, 3+15, 136)-Net over F81 — Digital
Digital (3, 18, 136)-net over F81, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
(3, 3+15, 1819)-Net in Base 81 — Upper bound on s
There is no (3, 18, 1820)-net in base 81, because
- 1 times m-reduction [i] would yield (3, 17, 1820)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 278 515836 044810 352014 154492 603201 > 8117 [i]