MinT - Best Known (39, 39+112, s)-Nets in Base 8

Best Known (39, 39+112, s)-Nets in Base 8

(39, 39+112, 98)-Net over F₈ — Constructive and digital

Digital (39, 151, 98)-net over F₈, using

t-expansion [i] based on digital (37, 151, 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+112, 129)-Net over F₈ — Digital

Digital (39, 151, 129)-net over F₈, using

t-expansion [i] based on digital (38, 151, 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+112, 809)-Net in Base 8 — Upper bound on s

There is no (39, 151, 810)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23944 273508 553443 127534 952313 760035 172994 031903 471620 316088 557531 553492 455107 091192 177897 191880 886661 881203 680217 666564 008088 980871 870800 > 8¹⁵¹ [i]