MinT - Best Known (39, 39+41, s)-Nets in Base 8

Best Known (39, 39+41, s)-Nets in Base 8

(39, 39+41, 98)-Net over F₈ — Constructive and digital

Digital (39, 80, 98)-net over F₈, using

t-expansion [i] based on digital (37, 80, 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]

(39, 39+41, 132)-Net over F₈ — Digital

Digital (39, 80, 132)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+41, 4367)-Net in Base 8 — Upper bound on s

There is no (39, 80, 4368)-net in base 8, because

1 times m-reduction [i] would yield (39, 79, 4368)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 221822 228314 062290 712462 736178 124357 029133 590097 237717 742849 719666 276688 > 8⁷⁹ [i]