MinT - Best Known (129−55, 129, s)-Nets in Base 4

Best Known (129−55, 129, s)-Nets in Base 4

(129−55, 129, 130)-Net over F₄ — Constructive and digital

Digital (74, 129, 130)-net over F₄, using

7 times m-reduction [i] based on digital (74, 136, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 68, 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]

(129−55, 129, 163)-Net over F₄ — Digital

Digital (74, 129, 163)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−55, 129, 2581)-Net in Base 4 — Upper bound on s

There is no (74, 129, 2582)-net in base 4, because

1 times m-reduction [i] would yield (74, 128, 2582)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 116755 335210 228462 447879 221657 552549 604588 538240 803658 752440 951682 155396 556160 > 4¹²⁸ [i]