Best Known (8, 8+60, s)-Nets in Base 81
(8, 8+60, 172)-Net over F81 — Constructive and digital
Digital (8, 68, 172)-net over F81, using
- t-expansion [i] based on digital (7, 68, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(8, 8+60, 226)-Net over F81 — Digital
Digital (8, 68, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
(8, 8+60, 3173)-Net in Base 81 — Upper bound on s
There is no (8, 68, 3174)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 5999 421587 732392 697659 990771 751704 559620 478725 739096 982458 775346 260970 158427 727310 903180 545713 815820 077788 387469 554259 790890 017601 > 8168 [i]