MinT - Best Known (58, 58+93, s)-Nets in Base 8

Best Known (58, 58+93, s)-Nets in Base 8

(58, 58+93, 98)-Net over F₈ — Constructive and digital

Digital (58, 151, 98)-net over F₈, using

t-expansion [i] based on digital (37, 151, 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+93, 144)-Net over F₈ — Digital

Digital (58, 151, 144)-net over F₈, using

t-expansion [i] based on digital (45, 151, 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+93, 2235)-Net in Base 8 — Upper bound on s

There is no (58, 151, 2236)-net in base 8, because

1 times m-reduction [i] would yield (58, 150, 2236)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2928 949302 601336 949957 300613 551640 664270 886123 383316 479156 097331 998128 341395 221557 429281 821079 164380 697894 651078 037411 759306 311473 095892 > 8¹⁵⁰ [i]