MinT - Best Known (50, 50+67, s)-Nets in Base 8

Best Known (50, 50+67, s)-Nets in Base 8

(50, 50+67, 98)-Net over F₈ — Constructive and digital

Digital (50, 117, 98)-net over F₈, using

t-expansion [i] based on digital (37, 117, 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+67, 144)-Net over F₈ — Digital

Digital (50, 117, 144)-net over F₈, using

t-expansion [i] based on digital (45, 117, 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+67, 2789)-Net in Base 8 — Upper bound on s

There is no (50, 117, 2790)-net in base 8, because

1 times m-reduction [i] would yield (50, 116, 2790)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 575 788347 427525 380364 187307 688102 858005 246766 026998 623875 616172 387244 317678 474402 179276 292328 854706 093585 > 8¹¹⁶ [i]