MinT - Best Known (54, 54+88, s)-Nets in Base 8

Best Known (54, 54+88, s)-Nets in Base 8

(54, 54+88, 98)-Net over F₈ — Constructive and digital

Digital (54, 142, 98)-net over F₈, using

t-expansion [i] based on digital (37, 142, 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+88, 144)-Net over F₈ — Digital

Digital (54, 142, 144)-net over F₈, using

t-expansion [i] based on digital (45, 142, 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+88, 1996)-Net in Base 8 — Upper bound on s

There is no (54, 142, 1997)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 501788 852299 068022 746356 239947 440353 062221 541713 560003 928426 239288 551483 082756 399644 056073 963623 359104 083526 907427 985102 663442 > 8¹⁴² [i]