MinT - Best Known (50, 50+69, s)-Nets in Base 8

Best Known (50, 50+69, s)-Nets in Base 8

(50, 50+69, 98)-Net over F₈ — Constructive and digital

Digital (50, 119, 98)-net over F₈, using

t-expansion [i] based on digital (37, 119, 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+69, 144)-Net over F₈ — Digital

Digital (50, 119, 144)-net over F₈, using

t-expansion [i] based on digital (45, 119, 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+69, 2612)-Net in Base 8 — Upper bound on s

There is no (50, 119, 2613)-net in base 8, because

1 times m-reduction [i] would yield (50, 118, 2613)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36796 851438 901597 648358 761378 792608 758936 892346 595255 869964 030294 952793 505580 579347 655451 865011 776207 289778 > 8¹¹⁸ [i]