MinT - Best Known (156−115, 156, s)-Nets in Base 8

Best Known (156−115, 156, s)-Nets in Base 8

(156−115, 156, 98)-Net over F₈ — Constructive and digital

Digital (41, 156, 98)-net over F₈, using

t-expansion [i] based on digital (37, 156, 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]

(156−115, 156, 129)-Net over F₈ — Digital

Digital (41, 156, 129)-net over F₈, using

t-expansion [i] based on digital (38, 156, 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]

(156−115, 156, 865)-Net in Base 8 — Upper bound on s

There is no (41, 156, 866)-net in base 8, because

1 times m-reduction [i] would yield (41, 155, 866)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 100 389225 000328 531969 834264 001528 970953 830172 338009 583815 855567 966463 863017 667392 771822 450994 794052 123020 105880 253232 676344 422808 767444 218616 > 8¹⁵⁵ [i]