MinT - Best Known (146−93, 146, s)-Nets in Base 8

Best Known (146−93, 146, s)-Nets in Base 8

(146−93, 146, 98)-Net over F₈ — Constructive and digital

Digital (53, 146, 98)-net over F₈, using

t-expansion [i] based on digital (37, 146, 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]

(146−93, 146, 144)-Net over F₈ — Digital

Digital (53, 146, 144)-net over F₈, using

t-expansion [i] based on digital (45, 146, 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]

(146−93, 146, 1777)-Net in Base 8 — Upper bound on s

There is no (53, 146, 1778)-net in base 8, because

1 times m-reduction [i] would yield (53, 145, 1778)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 89792 981093 992922 867493 524539 892442 807706 568832 389971 657687 215368 948028 754713 018776 091256 020870 997412 527937 778015 824315 415204 050760 > 8¹⁴⁵ [i]