MinT - Best Known (54, 54+76, s)-Nets in Base 8

Best Known (54, 54+76, s)-Nets in Base 8

(54, 54+76, 98)-Net over F₈ — Constructive and digital

Digital (54, 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]

(54, 54+76, 144)-Net over F₈ — Digital

Digital (54, 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]

(54, 54+76, 2613)-Net in Base 8 — Upper bound on s

There is no (54, 130, 2614)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2528 057959 996104 367657 468734 482796 275642 526432 904795 493841 334596 185137 757436 996557 133301 398022 567467 598678 812470 029880 > 8¹³⁰ [i]