Best Known (7, 58, s)-Nets in Base 81
(7, 58, 172)-Net over F81 — Constructive and digital
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
(7, 58, 190)-Net over F81 — Digital
Digital (7, 58, 190)-net over F81, using
- t-expansion [i] based on digital (6, 58, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(7, 58, 2844)-Net in Base 81 — Upper bound on s
There is no (7, 58, 2845)-net in base 81, because
- 1 times m-reduction [i] would yield (7, 57, 2845)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 6 102501 735466 239644 594667 972316 230709 847312 310378 433149 782987 010100 866228 181545 017183 498645 138735 013960 890001 > 8157 [i]