Best Known (82−74, 82, s)-Nets in Base 81
(82−74, 82, 172)-Net over F81 — Constructive and digital
Digital (8, 82, 172)-net over F81, using
- t-expansion [i] based on digital (7, 82, 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
(82−74, 82, 226)-Net over F81 — Digital
Digital (8, 82, 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
(82−74, 82, 3089)-Net in Base 81 — Upper bound on s
There is no (8, 82, 3090)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 159892 370996 277634 880319 306249 719514 180878 911264 118714 672640 103149 625941 219293 540697 007516 563626 442305 315008 771913 995349 627441 302464 871495 703217 522609 274401 > 8182 [i]