MinT - Best Known (113, 113+46, s)-Nets in Base 4

Best Known (113, 113+46, s)-Nets in Base 4

(113, 113+46, 531)-Net over F₄ — Constructive and digital

Digital (113, 159, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 53, 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]

(113, 113+46, 803)-Net over F₄ — Digital

Digital (113, 159, 803)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+46, 45627)-Net in Base 4 — Upper bound on s

There is no (113, 159, 45628)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534198 136122 278701 088517 178858 935478 635717 228599 585218 557766 575483 014912 285623 467367 436068 264630 > 4¹⁵⁹ [i]