MinT - Best Known (50, 50+72, s)-Nets in Base 8

Best Known (50, 50+72, s)-Nets in Base 8

(50, 50+72, 98)-Net over F₈ — Constructive and digital

Digital (50, 122, 98)-net over F₈, using

t-expansion [i] based on digital (37, 122, 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+72, 144)-Net over F₈ — Digital

Digital (50, 122, 144)-net over F₈, using

t-expansion [i] based on digital (45, 122, 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+72, 2322)-Net in Base 8 — Upper bound on s

There is no (50, 122, 2323)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 152 047202 568363 307454 637085 074066 622715 037758 257543 854144 853564 366438 632038 366248 658895 875717 587436 529079 077344 > 8¹²² [i]