MinT - Best Known (129−49, 129, s)-Nets in Base 4

Best Known (129−49, 129, s)-Nets in Base 4

(129−49, 129, 130)-Net over F₄ — Constructive and digital

Digital (80, 129, 130)-net over F₄, using

19 times m-reduction [i] based on 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]

(129−49, 129, 240)-Net over F₄ — Digital

Digital (80, 129, 240)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−49, 129, 5292)-Net in Base 4 — Upper bound on s

There is no (80, 129, 5293)-net in base 4, because

1 times m-reduction [i] would yield (80, 128, 5293)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 116231 817554 945512 585233 607433 951959 460204 597905 234616 679264 381386 960167 891534 > 4¹²⁸ [i]