Best Known (3, 3+19, s)-Nets in Base 81
(3, 3+19, 116)-Net over F81 — Constructive and digital
Digital (3, 22, 116)-net over F81, using
- t-expansion [i] based on digital (2, 22, 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+19, 136)-Net over F81 — Digital
Digital (3, 22, 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+19, 1467)-Net in Base 81 — Upper bound on s
There is no (3, 22, 1468)-net in base 81, because
- 1 times m-reduction [i] would yield (3, 21, 1468)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 12009 060177 925788 587514 176106 351090 055361 > 8121 [i]