MinT - Best Known (151−107, 151, s)-Nets in Base 8

Best Known (151−107, 151, s)-Nets in Base 8

(151−107, 151, 98)-Net over F₈ — Constructive and digital

Digital (44, 151, 98)-net over F₈, using

t-expansion [i] based on digital (37, 151, 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]

(151−107, 151, 130)-Net over F₈ — Digital

Digital (44, 151, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(151−107, 151, 1025)-Net in Base 8 — Upper bound on s

There is no (44, 151, 1026)-net in base 8, because

1 times m-reduction [i] would yield (44, 150, 1026)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3049 668483 418273 696674 048419 075710 328967 117107 145182 861909 698989 961058 998794 397855 169757 461807 559762 621677 439927 095629 717422 188044 722432 > 8¹⁵⁰ [i]