MinT - Best Known (53, 53+91, s)-Nets in Base 8

Best Known (53, 53+91, s)-Nets in Base 8

(53, 53+91, 98)-Net over F₈ — Constructive and digital

Digital (53, 144, 98)-net over F₈, using

t-expansion [i] based on digital (37, 144, 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]

(53, 53+91, 144)-Net over F₈ — Digital

Digital (53, 144, 144)-net over F₈, using

t-expansion [i] based on digital (45, 144, 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]

(53, 53+91, 1837)-Net in Base 8 — Upper bound on s

There is no (53, 144, 1838)-net in base 8, because

1 times m-reduction [i] would yield (53, 143, 1838)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1398 751471 185885 921814 079467 265688 193680 055134 243848 060723 380176 681582 620537 218846 922294 772032 287848 336722 809857 264648 287062 711591 > 8¹⁴³ [i]