MinT - Best Known (81−41, 81, s)-Nets in Base 8

Best Known (81−41, 81, s)-Nets in Base 8

(81−41, 81, 98)-Net over F₈ — Constructive and digital

Digital (40, 81, 98)-net over F₈, using

t-expansion [i] based on digital (37, 81, 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]

(81−41, 81, 141)-Net over F₈ — Digital

Digital (40, 81, 141)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(81−41, 81, 4846)-Net in Base 8 — Upper bound on s

There is no (40, 81, 4847)-net in base 8, because

1 times m-reduction [i] would yield (40, 80, 4847)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 767645 034838 014154 009279 076581 316927 187885 373140 680344 891339 595056 001526 > 8⁸⁰ [i]