Best Known (66, 66+106, s)-Nets in Base 8
(66, 66+106, 98)-Net over F8 — Constructive and digital
Digital (66, 172, 98)-net over F8, using
- t-expansion [i] based on digital (37, 172, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
(66, 66+106, 144)-Net over F8 — Digital
Digital (66, 172, 144)-net over F8, using
- t-expansion [i] based on digital (45, 172, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(66, 66+106, 2475)-Net in Base 8 — Upper bound on s
There is no (66, 172, 2476)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 217172 946356 957482 435326 501114 028583 623115 443468 927987 875155 746613 454313 115909 671075 914451 349159 720048 882242 666698 680789 157338 020910 999396 579985 157180 850352 > 8172 [i]