MinT - Best Known (137−80, 137, s)-Nets in Base 8

Best Known (137−80, 137, s)-Nets in Base 8

(137−80, 137, 98)-Net over F₈ — Constructive and digital

Digital (57, 137, 98)-net over F₈, using

t-expansion [i] based on digital (37, 137, 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]

(137−80, 137, 144)-Net over F₈ — Digital

Digital (57, 137, 144)-net over F₈, using

t-expansion [i] based on digital (45, 137, 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]

(137−80, 137, 2765)-Net in Base 8 — Upper bound on s

There is no (57, 137, 2766)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5291 427104 601177 093444 517797 106095 485745 587251 231816 697867 665288 132910 508338 818336 841743 541197 142393 485429 258224 109469 129430 > 8¹³⁷ [i]