Best Known (68, 68+93, s)-Nets in Base 8
(68, 68+93, 100)-Net over F8 — Constructive and digital
Digital (68, 161, 100)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 54, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (14, 107, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (8, 54, 35)-net over F8, using
(68, 68+93, 146)-Net over F8 — Digital
Digital (68, 161, 146)-net over F8, using
(68, 68+93, 156)-Net in Base 8
(68, 161, 156)-net in base 8, using
- 3 times m-reduction [i] based on (68, 164, 156)-net in base 8, using
- base change [i] based on digital (27, 123, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- base change [i] based on digital (27, 123, 156)-net over F16, using
(68, 68+93, 3529)-Net in Base 8 — Upper bound on s
There is no (68, 161, 3530)-net in base 8, because
- 1 times m-reduction [i] would yield (68, 160, 3530)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 3 126255 287376 562400 425803 028522 187034 655690 403424 516188 360049 137672 000227 581861 609369 312394 265016 426211 965492 477226 977102 446938 739542 736241 791520 > 8160 [i]