Best Known (62−49, 62, s)-Nets in Base 81
(62−49, 62, 224)-Net over F81 — Constructive and digital
Digital (13, 62, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
(62−49, 62, 298)-Net over F81 — Digital
Digital (13, 62, 298)-net over F81, using
- t-expansion [i] based on digital (12, 62, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(62−49, 62, 8677)-Net in Base 81 — Upper bound on s
There is no (13, 62, 8678)-net in base 81, because
- 1 times m-reduction [i] would yield (13, 61, 8678)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 261 628453 716526 768186 662020 016945 873048 389103 095516 311693 650132 486266 746081 484416 193054 967659 032720 228555 807844 860161 > 8161 [i]