MinT - Best Known (141−89, 141, s)-Nets in Base 8

Best Known (141−89, 141, s)-Nets in Base 8

(141−89, 141, 98)-Net over F₈ — Constructive and digital

Digital (52, 141, 98)-net over F₈, using

t-expansion [i] based on digital (37, 141, 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]

(141−89, 141, 144)-Net over F₈ — Digital

Digital (52, 141, 144)-net over F₈, using

t-expansion [i] based on digital (45, 141, 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]

(141−89, 141, 1814)-Net in Base 8 — Upper bound on s

There is no (52, 141, 1815)-net in base 8, because

1 times m-reduction [i] would yield (52, 140, 1815)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 749746 656732 387711 686667 320136 179153 785245 961458 917733 125660 958809 614281 025452 525537 907686 106982 110181 138682 968465 584272 429232 > 8¹⁴⁰ [i]