MinT - Best Known (111, 111+44, s)-Nets in Base 4

Best Known (111, 111+44, s)-Nets in Base 4

(111, 111+44, 531)-Net over F₄ — Constructive and digital

Digital (111, 155, 531)-net over F₄, using

1 times m-reduction [i] based on digital (111, 156, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 52, 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]

(111, 111+44, 854)-Net over F₄ — Digital

Digital (111, 155, 854)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+44, 52646)-Net in Base 4 — Upper bound on s

There is no (111, 155, 52647)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2086 201720 565401 800465 022243 575814 262779 383020 301597 268684 885107 042021 763231 103707 176320 424310 > 4¹⁵⁵ [i]