MinT - Best Known (135−78, 135, s)-Nets in Base 8

Best Known (135−78, 135, s)-Nets in Base 8

(135−78, 135, 98)-Net over F₈ — Constructive and digital

Digital (57, 135, 98)-net over F₈, using

t-expansion [i] based on digital (37, 135, 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]

(135−78, 135, 144)-Net over F₈ — Digital

Digital (57, 135, 144)-net over F₈, using

t-expansion [i] based on digital (45, 135, 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]

(135−78, 135, 2915)-Net in Base 8 — Upper bound on s

There is no (57, 135, 2916)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 82 740150 549482 962988 837338 507017 950723 434632 539760 303495 730096 030875 906764 918608 096651 883600 530165 351634 771434 995592 203280 > 8¹³⁵ [i]