MinT - Best Known (54, 54+70, s)-Nets in Base 8

Best Known (54, 54+70, s)-Nets in Base 8

(54, 54+70, 98)-Net over F₈ — Constructive and digital

Digital (54, 124, 98)-net over F₈, using

t-expansion [i] based on digital (37, 124, 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+70, 144)-Net over F₈ — Digital

Digital (54, 124, 144)-net over F₈, using

t-expansion [i] based on digital (45, 124, 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+70, 3123)-Net in Base 8 — Upper bound on s

There is no (54, 124, 3124)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9672 239365 410744 053751 775181 788341 075043 323879 397435 300334 697950 925926 017507 929747 437969 776406 892335 359496 761881 > 8¹²⁴ [i]