Best Known (128−91, 128, s)-Nets in Base 8
(128−91, 128, 98)-Net over F8 — Constructive and digital
Digital (37, 128, 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
(128−91, 128, 121)-Net over F8 — Digital
Digital (37, 128, 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
(128−91, 128, 862)-Net in Base 8 — Upper bound on s
There is no (37, 128, 863)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 127, 863)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 5 006366 673358 842077 047860 745108 768143 645775 868854 736347 528064 786127 025738 809001 568554 256816 585254 448849 853340 864764 > 8127 [i]