Best Known (80−47, 80, s)-Nets in Base 81
(80−47, 80, 370)-Net over F81 — Constructive and digital
Digital (33, 80, 370)-net over F81, using
- t-expansion [i] based on digital (16, 80, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(80−47, 80, 576)-Net over F81 — Digital
Digital (33, 80, 576)-net over F81, using
- net from sequence [i] based on digital (33, 575)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 33 and N(F) ≥ 576, using
(80−47, 80, 423239)-Net in Base 81 — Upper bound on s
There is no (33, 80, 423240)-net in base 81, because
- 1 times m-reduction [i] would yield (33, 79, 423240)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 5 892992 550568 599615 272272 113015 819404 080291 526383 206300 839347 345108 681194 402057 454237 692367 120981 586480 460924 370130 985940 603084 131990 977911 039170 185601 > 8179 [i]