MinT - Best Known (115−75, 115, s)-Nets in Base 8

Best Known (115−75, 115, s)-Nets in Base 8

(115−75, 115, 98)-Net over F₈ — Constructive and digital

Digital (40, 115, 98)-net over F₈, using

t-expansion [i] based on digital (37, 115, 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]

(115−75, 115, 129)-Net over F₈ — Digital

Digital (40, 115, 129)-net over F₈, using

t-expansion [i] based on digital (38, 115, 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]

(115−75, 115, 1245)-Net in Base 8 — Upper bound on s

There is no (40, 115, 1246)-net in base 8, because

1 times m-reduction [i] would yield (40, 114, 1246)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9 119004 865092 052421 178845 647665 653070 571574 990761 423292 613403 349781 529968 757542 951626 861375 459450 922774 > 8¹¹⁴ [i]