MinT - Best Known (58, 58+89, s)-Nets in Base 8

Best Known (58, 58+89, s)-Nets in Base 8

(58, 58+89, 98)-Net over F₈ — Constructive and digital

Digital (58, 147, 98)-net over F₈, using

t-expansion [i] based on digital (37, 147, 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+89, 144)-Net over F₈ — Digital

Digital (58, 147, 144)-net over F₈, using

t-expansion [i] based on digital (45, 147, 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+89, 2418)-Net in Base 8 — Upper bound on s

There is no (58, 147, 2419)-net in base 8, because

1 times m-reduction [i] would yield (58, 146, 2419)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 719761 854157 591824 506286 173294 286810 584020 016296 608624 109848 271656 623178 975389 745194 634008 477039 263195 011986 635885 056899 979263 125860 > 8¹⁴⁶ [i]