MinT - Best Known (116, 116+38, s)-Nets in Base 4

Best Known (116, 116+38, s)-Nets in Base 4

(116, 116+38, 1028)-Net over F₄ — Constructive and digital

Digital (116, 154, 1028)-net over F₄, using

4² times duplication [i] based on digital (114, 152, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 38, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(116, 116+38, 1584)-Net over F₄ — Digital

Digital (116, 154, 1584)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+38, 200408)-Net in Base 4 — Upper bound on s

There is no (116, 154, 200409)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 516082 640767 504931 366389 293718 643542 636869 052888 737622 685069 586982 502869 687308 855913 848872 > 4¹⁵⁴ [i]