MinT - Best Known (54, 54+74, s)-Nets in Base 8

Best Known (54, 54+74, s)-Nets in Base 8

(54, 54+74, 98)-Net over F₈ — Constructive and digital

Digital (54, 128, 98)-net over F₈, using

t-expansion [i] based on digital (37, 128, 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+74, 144)-Net over F₈ — Digital

Digital (54, 128, 144)-net over F₈, using

t-expansion [i] based on digital (45, 128, 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+74, 2763)-Net in Base 8 — Upper bound on s

There is no (54, 128, 2764)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 39 926761 984630 893999 230253 889106 067963 134925 851719 852916 193661 438492 815079 921635 037011 091926 565894 592133 920495 660772 > 8¹²⁸ [i]