MinT - Best Known (144−85, 144, s)-Nets in Base 8

Best Known (144−85, 144, s)-Nets in Base 8

(144−85, 144, 98)-Net over F₈ — Constructive and digital

Digital (59, 144, 98)-net over F₈, using

t-expansion [i] based on digital (37, 144, 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]

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

Digital (59, 144, 144)-net over F₈, using

t-expansion [i] based on digital (45, 144, 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]

(144−85, 144, 2775)-Net in Base 8 — Upper bound on s

There is no (59, 144, 2776)-net in base 8, because

1 times m-reduction [i] would yield (59, 143, 2776)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1389 506075 074454 133751 986568 159057 014957 851888 241320 742148 743893 964359 977445 175798 851846 541044 107377 931045 917208 037776 007399 481460 > 8¹⁴³ [i]