MinT - Best Known (143, 143+62, s)-Nets in Base 4

Best Known (143, 143+62, s)-Nets in Base 4

(143, 143+62, 450)-Net over F₄ — Constructive and digital

Digital (143, 205, 450)-net over F₄, using

1 times m-reduction [i] based on digital (143, 206, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 103, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(143, 143+62, 819)-Net over F₄ — Digital

Digital (143, 205, 819)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+62, 39627)-Net in Base 4 — Upper bound on s

There is no (143, 205, 39628)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2644 878588 876093 215432 756228 256863 514300 490231 744640 854967 956218 346683 147264 329025 760223 541679 377128 891071 163259 367469 873680 > 4²⁰⁵ [i]