MinT - Best Known (151−57, 151, s)-Nets in Base 4

Best Known (151−57, 151, s)-Nets in Base 4

(151−57, 151, 130)-Net over F₄ — Constructive and digital

Digital (94, 151, 130)-net over F₄, using

25 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 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]

(151−57, 151, 280)-Net over F₄ — Digital

Digital (94, 151, 280)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−57, 151, 6304)-Net in Base 4 — Upper bound on s

There is no (94, 151, 6305)-net in base 4, because

1 times m-reduction [i] would yield (94, 150, 6305)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 043310 612924 927069 889702 932845 411476 038945 168544 394081 324613 052854 926053 094665 950995 780760 > 4¹⁵⁰ [i]