MinT - Best Known (58, 58+97, s)-Nets in Base 8

Best Known (58, 58+97, s)-Nets in Base 8

(58, 58+97, 98)-Net over F₈ — Constructive and digital

Digital (58, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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]

(58, 58+97, 144)-Net over F₈ — Digital

Digital (58, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 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]

(58, 58+97, 2083)-Net in Base 8 — Upper bound on s

There is no (58, 155, 2084)-net in base 8, because

1 times m-reduction [i] would yield (58, 154, 2084)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 969041 355932 778267 348121 153878 404813 164356 940009 719500 612766 352557 457284 377600 977436 128607 321899 485997 463988 991814 727908 617774 035470 738560 > 8¹⁵⁴ [i]