MinT - Best Known (50, 50+74, s)-Nets in Base 8

Best Known (50, 50+74, s)-Nets in Base 8

(50, 50+74, 98)-Net over F₈ — Constructive and digital

Digital (50, 124, 98)-net over F₈, using

t-expansion [i] based on digital (37, 124, 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]

(50, 50+74, 144)-Net over F₈ — Digital

Digital (50, 124, 144)-net over F₈, using

t-expansion [i] based on digital (45, 124, 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]

(50, 50+74, 2202)-Net in Base 8 — Upper bound on s

There is no (50, 124, 2203)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9768 972578 613388 234907 087198 024364 661592 001879 355842 398574 068244 576045 401089 006669 056681 022487 018944 234053 101232 > 8¹²⁴ [i]