MinT - Best Known (56, 154, s)-Nets in Base 8

Best Known (56, 154, s)-Nets in Base 8

(56, 154, 98)-Net over F₈ — Constructive and digital

Digital (56, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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, 154, 144)-Net over F₈ — Digital

Digital (56, 154, 144)-net over F₈, using

t-expansion [i] based on digital (45, 154, 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, 154, 1850)-Net in Base 8 — Upper bound on s

There is no (56, 154, 1851)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 031450 834097 883022 955193 090907 356425 291569 589116 195591 836295 811138 947496 076620 685534 276911 939181 041731 775363 941370 627361 895789 964638 044186 > 8¹⁵⁴ [i]