MinT - Best Known (58, 58+103, s)-Nets in Base 8

Best Known (58, 58+103, s)-Nets in Base 8

(58, 58+103, 98)-Net over F₈ — Constructive and digital

Digital (58, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 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+103, 144)-Net over F₈ — Digital

Digital (58, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 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+103, 1899)-Net in Base 8 — Upper bound on s

There is no (58, 161, 1900)-net in base 8, because

1 times m-reduction [i] would yield (58, 160, 1900)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 141441 473666 181707 765805 646316 444259 846907 109535 131230 371204 751902 082797 549933 631698 948074 339285 418619 358174 136520 598826 672079 413608 089636 919964 > 8¹⁶⁰ [i]