MinT - Best Known (145−93, 145, s)-Nets in Base 8

Best Known (145−93, 145, s)-Nets in Base 8

(145−93, 145, 98)-Net over F₈ — Constructive and digital

Digital (52, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(145−93, 145, 144)-Net over F₈ — Digital

Digital (52, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 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]

(145−93, 145, 1697)-Net in Base 8 — Upper bound on s

There is no (52, 145, 1698)-net in base 8, because

1 times m-reduction [i] would yield (52, 144, 1698)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11181 598425 676789 502822 092440 041211 707601 158201 791493 501696 102766 530774 696756 891416 598431 091174 116355 242181 437363 355315 002364 461504 > 8¹⁴⁴ [i]