MinT - Best Known (107−62, 107, s)-Nets in Base 8

Best Known (107−62, 107, s)-Nets in Base 8

(107−62, 107, 98)-Net over F₈ — Constructive and digital

Digital (45, 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]

(107−62, 107, 144)-Net over F₈ — Digital

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]

(107−62, 107, 2303)-Net in Base 8 — Upper bound on s

There is no (45, 107, 2304)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 292778 375227 020715 413650 311619 640940 993251 266159 701911 590179 260733 258328 355656 954841 669065 997809 > 8¹⁰⁷ [i]