MinT - Best Known (130−78, 130, s)-Nets in Base 8

Best Known (130−78, 130, s)-Nets in Base 8

(130−78, 130, 98)-Net over F₈ — Constructive and digital

Digital (52, 130, 98)-net over F₈, using

t-expansion [i] based on digital (37, 130, 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]

(130−78, 130, 144)-Net over F₈ — Digital

Digital (52, 130, 144)-net over F₈, using

t-expansion [i] based on digital (45, 130, 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]

(130−78, 130, 2227)-Net in Base 8 — Upper bound on s

There is no (52, 130, 2228)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2529 823956 616644 018110 004595 030617 092687 792682 874694 701323 421922 645849 302843 012562 958467 432886 010275 554827 329030 092676 > 8¹³⁰ [i]