Best Known (8, 8+28, s)-Nets in Base 81
(8, 8+28, 172)-Net over F81 — Constructive and digital
Digital (8, 36, 172)-net over F81, using
- t-expansion [i] based on digital (7, 36, 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+28, 226)-Net over F81 — Digital
Digital (8, 36, 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+28, 6101)-Net in Base 81 — Upper bound on s
There is no (8, 36, 6102)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 508 286100 759304 775351 996718 499150 735892 312564 436232 365084 955446 853441 > 8136 [i]