MinT - Best Known (114, 114+68, s)-Nets in Base 4

Best Known (114, 114+68, s)-Nets in Base 4

(114, 114+68, 135)-Net over F₄ — Constructive and digital

Digital (114, 182, 135)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (0, 34, 5)-net over F₄, using
  - net from sequence [i] based on digital (0, 4)-sequence over F₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 0 and N(F) ≥ 5, using
      - the rational function field F₄(x) [i]
    - Niederreiter sequence [i]
2. digital (80, 148, 130)-net over F₄, using
  - trace code for nets [i] based on digital (6, 74, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(114, 114+68, 340)-Net over F₄ — Digital

Digital (114, 182, 340)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+68, 7508)-Net in Base 4 — Upper bound on s

There is no (114, 182, 7509)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 696747 236408 414920 332153 402626 722863 966554 444068 508409 032100 222160 289083 983178 757320 884042 548532 660778 877772 > 4¹⁸² [i]