Best Known (8, 58, s)-Nets in Base 81
(8, 58, 172)-Net over F81 — Constructive and digital
Digital (8, 58, 172)-net over F81, using
- t-expansion [i] based on digital (7, 58, 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, 58, 226)-Net over F81 — Digital
Digital (8, 58, 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, 58, 3393)-Net in Base 81 — Upper bound on s
There is no (8, 58, 3394)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 493 956071 789757 543685 248624 863840 084551 854557 736554 056937 287166 456318 724418 802802 044205 014476 882877 791715 588001 > 8158 [i]