Best Known (41, 41+68, s)-Nets in Base 8
(41, 41+68, 98)-Net over F8 — Constructive and digital
Digital (41, 109, 98)-net over F8, using
- t-expansion [i] based on digital (37, 109, 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
(41, 41+68, 129)-Net over F8 — Digital
Digital (41, 109, 129)-net over F8, using
- t-expansion [i] based on digital (38, 109, 129)-net over F8, using
- net from sequence [i] based on digital (38, 128)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 38 and N(F) ≥ 129, using
- net from sequence [i] based on digital (38, 128)-sequence over F8, using
(41, 41+68, 1497)-Net in Base 8 — Upper bound on s
There is no (41, 109, 1498)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 274 609681 252013 755093 712387 850484 880204 027871 959415 641561 179868 305316 905087 060172 252287 273031 844744 > 8109 [i]