MinT - Best Known (129−50, 129, s)-Nets in Base 4

Best Known (129−50, 129, s)-Nets in Base 4

(129−50, 129, 130)-Net over F₄ — Constructive and digital

Digital (79, 129, 130)-net over F₄, using

17 times m-reduction [i] based on digital (79, 146, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 73, 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]

(129−50, 129, 225)-Net over F₄ — Digital

Digital (79, 129, 225)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−50, 129, 4316)-Net in Base 4 — Upper bound on s

There is no (79, 129, 4317)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 465440 267869 670133 269095 255534 595711 987931 715223 048998 552571 940466 110958 391920 > 4¹²⁹ [i]