MinT - Best Known (119, 143, s)-Nets in Base 4

Best Known (119, 143, s)-Nets in Base 4

(119, 143, 1542)-Net over F₄ — Constructive and digital

Digital (119, 143, 1542)-net over F₄, using

4¹ times duplication [i] based on digital (118, 142, 1542)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (34, 46, 514)-net over F₄, using
    - trace code for nets [i] based on digital (11, 23, 257)-net over F₁₆, using
      - base reduction for projective spaces (embedding PG(11,256) in PG(22,16)) for nets [i] based on digital (0, 12, 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 (72, 96, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 24, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(119, 143, 17412)-Net over F₄ — Digital

Digital (119, 143, 17412)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 143, large)-Net in Base 4 — Upper bound on s

There is no (119, 143, large)-net in base 4, because

22 times m-reduction [i] would yield (119, 121, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]