Best Known (82−54, 82, s)-Nets in Base 81
(82−54, 82, 370)-Net over F81 — Constructive and digital
Digital (28, 82, 370)-net over F81, using
- t-expansion [i] based on digital (16, 82, 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
(82−54, 82, 500)-Net over F81 — Digital
Digital (28, 82, 500)-net over F81, using
- t-expansion [i] based on digital (26, 82, 500)-net over F81, using
- net from sequence [i] based on digital (26, 499)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
- net from sequence [i] based on digital (26, 499)-sequence over F81, using
(82−54, 82, 85386)-Net in Base 81 — Upper bound on s
There is no (28, 82, 85387)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 132244 470767 881354 031812 403570 855009 405131 735811 897839 000541 369722 556505 106832 854866 018225 905887 959080 417317 094699 090021 877942 556825 001613 147471 838078 055121 > 8182 [i]