MinT - Best Known (50, 50+71, s)-Nets in Base 8

Best Known (50, 50+71, s)-Nets in Base 8

(50, 50+71, 98)-Net over F₈ — Constructive and digital

Digital (50, 121, 98)-net over F₈, using

t-expansion [i] based on digital (37, 121, 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+71, 144)-Net over F₈ — Digital

Digital (50, 121, 144)-net over F₈, using

t-expansion [i] based on digital (45, 121, 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+71, 2458)-Net in Base 8 — Upper bound on s

There is no (50, 121, 2459)-net in base 8, because

1 times m-reduction [i] would yield (50, 120, 2459)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 375587 411432 314249 000153 117443 518125 608071 429886 433823 785976 649664 358276 130137 934342 359704 322238 149871 064384 > 8¹²⁰ [i]