MinT - Best Known (50, 50+82, s)-Nets in Base 8

Best Known (50, 50+82, s)-Nets in Base 8

(50, 50+82, 98)-Net over F₈ — Constructive and digital

Digital (50, 132, 98)-net over F₈, using

t-expansion [i] based on digital (37, 132, 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+82, 144)-Net over F₈ — Digital

Digital (50, 132, 144)-net over F₈, using

t-expansion [i] based on digital (45, 132, 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+82, 1837)-Net in Base 8 — Upper bound on s

There is no (50, 132, 1838)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 162356 331709 423833 365711 596617 339138 752430 206857 571903 811018 197718 727894 642466 211162 597392 226995 293166 759254 849990 606133 > 8¹³² [i]