MinT - Best Known (111, 111+45, s)-Nets in Base 4

Best Known (111, 111+45, s)-Nets in Base 4

(111, 111+45, 531)-Net over F₄ — Constructive and digital

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+45, 802)-Net over F₄ — Digital

Digital (111, 156, 802)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+45, 52646)-Net in Base 4 — Upper bound on s

There is no (111, 156, 52647)-net in base 4, because

1 times m-reduction [i] would yield (111, 155, 52647)-net in base 4, but
- 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]