MinT - Best Known (56, 148, s)-Nets in Base 8

Best Known (56, 148, s)-Nets in Base 8

(56, 148, 98)-Net over F₈ — Constructive and digital

Digital (56, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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]

(56, 148, 144)-Net over F₈ — Digital

Digital (56, 148, 144)-net over F₈, using

t-expansion [i] based on digital (45, 148, 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]

(56, 148, 2039)-Net in Base 8 — Upper bound on s

There is no (56, 148, 2040)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 542787 524874 395962 479762 058296 225107 340596 274190 431787 107845 647397 858696 824808 868551 395337 224093 136512 096214 559774 471567 701553 025150 > 8¹⁴⁸ [i]