MinT - Best Known (112−66, 112, s)-Nets in Base 8

Best Known (112−66, 112, s)-Nets in Base 8

(112−66, 112, 98)-Net over F₈ — Constructive and digital

Digital (46, 112, 98)-net over F₈, using

t-expansion [i] based on digital (37, 112, 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]

(112−66, 112, 144)-Net over F₈ — Digital

Digital (46, 112, 144)-net over F₈, using

t-expansion [i] based on digital (45, 112, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(112−66, 112, 2163)-Net in Base 8 — Upper bound on s

There is no (46, 112, 2164)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 140987 176981 713749 719342 758285 012962 074675 435886 892540 611893 953979 761721 286418 867916 245808 948310 697125 > 8¹¹² [i]