Best Known (8, 8+70, s)-Nets in Base 81
(8, 8+70, 172)-Net over F81 — Constructive and digital
Digital (8, 78, 172)-net over F81, using
- t-expansion [i] based on digital (7, 78, 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+70, 226)-Net over F81 — Digital
Digital (8, 78, 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+70, 3096)-Net in Base 81 — Upper bound on s
There is no (8, 78, 3097)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 72796 737116 567544 938686 939391 398542 905658 428946 093384 388652 797992 207438 248643 431463 503641 422315 236376 666109 711365 806729 688233 402948 269530 516373 055601 > 8178 [i]