Best Known (163−105, 163, s)-Nets in Base 8
(163−105, 163, 98)-Net over F8 — Constructive and digital
Digital (58, 163, 98)-net over F8, using
- t-expansion [i] based on digital (37, 163, 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
(163−105, 163, 144)-Net over F8 — Digital
Digital (58, 163, 144)-net over F8, using
- t-expansion [i] based on digital (45, 163, 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
(163−105, 163, 1847)-Net in Base 8 — Upper bound on s
There is no (58, 163, 1848)-net in base 8, because
- 1 times m-reduction [i] would yield (58, 162, 1848)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 201 244422 750666 710696 845041 247489 388009 344720 600113 275220 443435 239563 451887 920884 949052 030886 837165 268889 991344 728424 302374 813014 319262 201693 039939 > 8162 [i]