MinT - Best Known (50, 50+77, s)-Nets in Base 8

Best Known (50, 50+77, s)-Nets in Base 8

(50, 50+77, 98)-Net over F₈ — Constructive and digital

Digital (50, 127, 98)-net over F₈, using

t-expansion [i] based on digital (37, 127, 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+77, 144)-Net over F₈ — Digital

Digital (50, 127, 144)-net over F₈, using

t-expansion [i] based on digital (45, 127, 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+77, 2095)-Net in Base 8 — Upper bound on s

There is no (50, 127, 2096)-net in base 8, because

1 times m-reduction [i] would yield (50, 126, 2096)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 623408 114440 212282 197773 611130 467181 442189 788309 942777 321875 123255 058997 267541 689941 728122 831310 476537 800425 470073 > 8¹²⁶ [i]