MinT - Best Known (133−78, 133, s)-Nets in Base 8

Best Known (133−78, 133, s)-Nets in Base 8

(133−78, 133, 98)-Net over F₈ — Constructive and digital

Digital (55, 133, 98)-net over F₈, using

t-expansion [i] based on digital (37, 133, 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]

(133−78, 133, 144)-Net over F₈ — Digital

Digital (55, 133, 144)-net over F₈, using

t-expansion [i] based on digital (45, 133, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(133−78, 133, 2618)-Net in Base 8 — Upper bound on s

There is no (55, 133, 2619)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 300901 549593 885400 322962 842891 067358 999510 222609 124431 090834 068697 687832 811175 585777 388194 872443 886379 104633 156479 477016 > 8¹³³ [i]