Best Known (41, 41+77, s)-Nets in Base 8
(41, 41+77, 98)-Net over F8 — Constructive and digital
Digital (41, 118, 98)-net over F8, using
- t-expansion [i] based on digital (37, 118, 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+77, 129)-Net over F8 — Digital
Digital (41, 118, 129)-net over F8, using
- t-expansion [i] based on digital (38, 118, 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+77, 1271)-Net in Base 8 — Upper bound on s
There is no (41, 118, 1272)-net in base 8, because
- 1 times m-reduction [i] would yield (41, 117, 1272)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 4694 396596 186375 015147 888412 670148 266366 767446 140722 521800 282592 444863 571554 909326 917455 375112 057891 168583 > 8117 [i]