MinT - Best Known (39, 39+96, s)-Nets in Base 8

Best Known (39, 39+96, s)-Nets in Base 8

(39, 39+96, 98)-Net over F₈ — Constructive and digital

Digital (39, 135, 98)-net over F₈, using

t-expansion [i] based on digital (37, 135, 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+96, 129)-Net over F₈ — Digital

Digital (39, 135, 129)-net over F₈, using

t-expansion [i] based on digital (38, 135, 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]

(39, 39+96, 898)-Net in Base 8 — Upper bound on s

There is no (39, 135, 899)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 86 475167 728998 524504 534877 627392 798229 279181 572721 857424 156861 003764 381442 944435 542613 934815 836885 662345 757639 478863 235320 > 8¹³⁵ [i]