MinT - Best Known (38, 78, s)-Nets in Base 8

Best Known (38, 78, s)-Nets in Base 8

(38, 78, 98)-Net over F₈ — Constructive and digital

Digital (38, 78, 98)-net over F₈, using

t-expansion [i] based on digital (37, 78, 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]

(38, 78, 130)-Net over F₈ — Digital

Digital (38, 78, 130)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 78, 3934)-Net in Base 8 — Upper bound on s

There is no (38, 78, 3935)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 27665 472327 534567 369087 026530 166257 165268 722056 663886 268285 571345 475067 > 8⁷⁸ [i]