MinT - Best Known (57, 57+82, s)-Nets in Base 8

Best Known (57, 57+82, s)-Nets in Base 8

(57, 57+82, 98)-Net over F₈ — Constructive and digital

Digital (57, 139, 98)-net over F₈, using

t-expansion [i] based on digital (37, 139, 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]

(57, 57+82, 144)-Net over F₈ — Digital

Digital (57, 139, 144)-net over F₈, using

t-expansion [i] based on digital (45, 139, 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]

(57, 57+82, 2631)-Net in Base 8 — Upper bound on s

There is no (57, 139, 2632)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 338747 353365 423450 603006 525432 338343 869728 052059 791851 969072 572405 106918 002685 258562 966987 542195 201864 771246 941588 993920 733560 > 8¹³⁹ [i]