MinT - Best Known (107−61, 107, s)-Nets in Base 8

Best Known (107−61, 107, s)-Nets in Base 8

(107−61, 107, 98)-Net over F₈ — Constructive and digital

Digital (46, 107, 98)-net over F₈, using

t-expansion [i] based on digital (37, 107, 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]

(107−61, 107, 144)-Net over F₈ — Digital

Digital (46, 107, 144)-net over F₈, using

t-expansion [i] based on digital (45, 107, 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]

(107−61, 107, 2651)-Net in Base 8 — Upper bound on s

There is no (46, 107, 2652)-net in base 8, because

1 times m-reduction [i] would yield (46, 106, 2652)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534878 199880 447695 045198 933509 642022 055807 523883 273672 768156 036841 249424 172249 774425 336746 289040 > 8¹⁰⁶ [i]