MinT - Best Known (39, 39+119, s)-Nets in Base 8

Best Known (39, 39+119, s)-Nets in Base 8

(39, 39+119, 98)-Net over F₈ — Constructive and digital

Digital (39, 158, 98)-net over F₈, using

t-expansion [i] based on digital (37, 158, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(39, 39+119, 129)-Net over F₈ — Digital

Digital (39, 158, 129)-net over F₈, using

t-expansion [i] based on digital (38, 158, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(39, 39+119, 787)-Net in Base 8 — Upper bound on s

There is no (39, 158, 788)-net in base 8, because

1 times m-reduction [i] would yield (39, 157, 788)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6125 999210 957339 657034 115078 811246 893856 852108 782669 003834 842444 173696 088349 004356 985395 046299 359402 616138 354367 500658 455767 980443 025305 496928 > 8¹⁵⁷ [i]