Best Known (3, 3+21, s)-Nets in Base 81
(3, 3+21, 116)-Net over F81 — Constructive and digital
Digital (3, 24, 116)-net over F81, using
- t-expansion [i] based on digital (2, 24, 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+21, 136)-Net over F81 — Digital
Digital (3, 24, 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+21, 1383)-Net in Base 81 — Upper bound on s
There is no (3, 24, 1384)-net in base 81, because
- 1 times m-reduction [i] would yield (3, 23, 1384)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 78 881664 120258 511584 910450 601204 589318 867201 > 8123 [i]