Best Known (80−68, 80, s)-Nets in Base 81
(80−68, 80, 172)-Net over F81 — Constructive and digital
Digital (12, 80, 172)-net over F81, using
- t-expansion [i] based on digital (7, 80, 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
(80−68, 80, 298)-Net over F81 — Digital
Digital (12, 80, 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
(80−68, 80, 5218)-Net in Base 81 — Upper bound on s
There is no (12, 80, 5219)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 479 337488 376983 199095 997915 368635 218635 789861 384355 137707 555683 746785 232223 232492 212377 369563 369537 940876 115620 925437 965310 735279 291952 789375 651915 571681 > 8180 [i]