MinT - Best Known (83−29, 83, s)-Nets in Base 4

Best Known (83−29, 83, s)-Nets in Base 4

(83−29, 83, 130)-Net over F₄ — Constructive and digital

Digital (54, 83, 130)-net over F₄, using

13 times m-reduction [i] based on digital (54, 96, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 48, 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]

(83−29, 83, 228)-Net over F₄ — Digital

Digital (54, 83, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−29, 83, 6760)-Net in Base 4 — Upper bound on s

There is no (54, 83, 6761)-net in base 4, because

1 times m-reduction [i] would yield (54, 82, 6761)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 413681 662312 277730 759688 679299 946249 972077 255568 > 4⁸² [i]