MinT - Best Known (131−88, 131, s)-Nets in Base 8

Best Known (131−88, 131, s)-Nets in Base 8

(131−88, 131, 98)-Net over F₈ — Constructive and digital

Digital (43, 131, 98)-net over F₈, using

t-expansion [i] based on digital (37, 131, 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]

(131−88, 131, 129)-Net over F₈ — Digital

Digital (43, 131, 129)-net over F₈, using

t-expansion [i] based on digital (38, 131, 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]

(131−88, 131, 1176)-Net in Base 8 — Upper bound on s

There is no (43, 131, 1177)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20733 867996 495173 326822 740516 080325 806645 062571 020993 690866 731806 070773 642234 645036 475765 748483 450411 449955 392717 637648 > 8¹³¹ [i]