MinT - Best Known (146−85, 146, s)-Nets in Base 8

Best Known (146−85, 146, s)-Nets in Base 8

(146−85, 146, 98)-Net over F₈ — Constructive and digital

Digital (61, 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]

(146−85, 146, 144)-Net over F₈ — Digital

Digital (61, 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]

(146−85, 146, 3067)-Net in Base 8 — Upper bound on s

There is no (61, 146, 3068)-net in base 8, because

1 times m-reduction [i] would yield (61, 145, 3068)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 89296 346865 340963 912839 621229 492840 867079 723935 410603 973905 884157 930248 087175 969532 477232 218457 011519 747483 003412 630892 640172 144625 > 8¹⁴⁵ [i]