MinT - Best Known (112−48, 112, s)-Nets in Base 8

Best Known (112−48, 112, s)-Nets in Base 8

(112−48, 112, 354)-Net over F₈ — Constructive and digital

Digital (64, 112, 354)-net over F₈, using

2 times m-reduction [i] based on digital (64, 114, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 57, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(112−48, 112, 366)-Net over F₈ — Digital

Digital (64, 112, 366)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−48, 112, 22929)-Net in Base 8 — Upper bound on s

There is no (64, 112, 22930)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 139999 654987 569614 033411 913581 602015 271815 978827 849669 538895 451347 757812 929668 637162 916221 481550 066736 > 8¹¹² [i]