Best Known (108−71, 108, s)-Nets in Base 8
(108−71, 108, 98)-Net over F8 — Constructive and digital
Digital (37, 108, 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
(108−71, 108, 121)-Net over F8 — Digital
Digital (37, 108, 121)-net over F8, using
- net from sequence [i] based on digital (37, 120)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 121, using
(108−71, 108, 1123)-Net in Base 8 — Upper bound on s
There is no (37, 108, 1124)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 107, 1124)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 4 304860 917193 143095 647282 532817 551913 096004 212384 766918 421679 396384 790776 087572 962377 624713 083121 > 8107 [i]