MinT - Best Known (107−66, 107, s)-Nets in Base 8

Best Known (107−66, 107, s)-Nets in Base 8

(107−66, 107, 98)-Net over F₈ — Constructive and digital

Digital (41, 107, 98)-net over F₈, using

t-expansion [i] based on digital (37, 107, 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]

(107−66, 107, 129)-Net over F₈ — Digital

Digital (41, 107, 129)-net over F₈, using

t-expansion [i] based on digital (38, 107, 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]

(107−66, 107, 1573)-Net in Base 8 — Upper bound on s

There is no (41, 107, 1574)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 338578 852088 222302 571867 403631 408305 462940 882472 728661 304855 026983 063014 195542 861971 029967 452515 > 8¹⁰⁷ [i]