MinT - Best Known (132, 159, s)-Nets in Base 4

Best Known (132, 159, s)-Nets in Base 4

(132, 159, 1542)-Net over F₄ — Constructive and digital

Digital (132, 159, 1542)-net over F₄, using

4¹ times duplication [i] based on digital (131, 158, 1542)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (37, 50, 514)-net over F₄, using
    - trace code for nets [i] based on digital (12, 25, 257)-net over F₁₆, using
      - base reduction for projective spaces (embedding PG(12,256) in PG(24,16)) for nets [i] based on digital (0, 13, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
  2. digital (81, 108, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 27, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(132, 159, 16917)-Net over F₄ — Digital

Digital (132, 159, 16917)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 159, large)-Net in Base 4 — Upper bound on s

There is no (132, 159, large)-net in base 4, because

25 times m-reduction [i] would yield (132, 134, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]