Best Known (79−66, 79, s)-Nets in Base 81
(79−66, 79, 224)-Net over F81 — Constructive and digital
Digital (13, 79, 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
(79−66, 79, 298)-Net over F81 — Digital
Digital (13, 79, 298)-net over F81, using
- t-expansion [i] based on digital (12, 79, 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
(79−66, 79, 6079)-Net in Base 81 — Upper bound on s
There is no (13, 79, 6080)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 5 898168 989246 218093 339973 484868 740110 221413 741353 255822 300407 638531 469100 401435 943138 901256 841931 603221 045054 333640 260834 136392 794556 429740 678643 379201 > 8179 [i]