MinT - Best Known (57, 57+84, s)-Nets in Base 8

Best Known (57, 57+84, s)-Nets in Base 8

(57, 57+84, 98)-Net over F₈ — Constructive and digital

Digital (57, 141, 98)-net over F₈, using

t-expansion [i] based on digital (37, 141, 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+84, 144)-Net over F₈ — Digital

Digital (57, 141, 144)-net over F₈, using

t-expansion [i] based on digital (45, 141, 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+84, 2511)-Net in Base 8 — Upper bound on s

There is no (57, 141, 2512)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 780974 631365 353476 702056 445209 168381 333026 640435 530174 105349 885503 795636 308229 676094 496839 703628 344771 728696 607448 580548 434678 > 8¹⁴¹ [i]