Best Known (25, 25+52, s)-Nets in Base 81
(25, 25+52, 370)-Net over F81 — Constructive and digital
Digital (25, 77, 370)-net over F81, using
- t-expansion [i] based on digital (16, 77, 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
(25, 25+52, 392)-Net over F81 — Digital
Digital (25, 77, 392)-net over F81, using
- net from sequence [i] based on digital (25, 391)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 25 and N(F) ≥ 392, using
(25, 25+52, 59178)-Net in Base 81 — Upper bound on s
There is no (25, 77, 59179)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 898 515388 790036 661280 990461 870561 612804 231062 088267 334165 657313 692611 595349 136961 450984 103983 886939 611443 614019 257301 648289 503903 363413 127599 892321 > 8177 [i]