MinT - Best Known (134−77, 134, s)-Nets in Base 8

Best Known (134−77, 134, s)-Nets in Base 8

(134−77, 134, 98)-Net over F₈ — Constructive and digital

Digital (57, 134, 98)-net over F₈, using

t-expansion [i] based on digital (37, 134, 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]

(134−77, 134, 144)-Net over F₈ — Digital

Digital (57, 134, 144)-net over F₈, using

t-expansion [i] based on digital (45, 134, 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]

(134−77, 134, 3084)-Net in Base 8 — Upper bound on s

There is no (57, 134, 3085)-net in base 8, because

1 times m-reduction [i] would yield (57, 133, 3085)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 300515 857653 695653 662471 730688 214979 317750 788889 539163 532723 755190 620152 018142 098961 096510 727535 831768 739872 392871 409024 > 8¹³³ [i]