MinT - Best Known (132−53, 132, s)-Nets in Base 4

Best Known (132−53, 132, s)-Nets in Base 4

(132−53, 132, 130)-Net over F₄ — Constructive and digital

Digital (79, 132, 130)-net over F₄, using

14 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]

(132−53, 132, 203)-Net over F₄ — Digital

Digital (79, 132, 203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−53, 132, 3777)-Net in Base 4 — Upper bound on s

There is no (79, 132, 3778)-net in base 4, because

1 times m-reduction [i] would yield (79, 131, 3778)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 435257 001321 962839 679224 651752 000760 570979 822796 607161 571712 225718 409015 890720 > 4¹³¹ [i]