MinT - Best Known (189−32, 189, s)-Nets in Base 4

Best Known (189−32, 189, s)-Nets in Base 4

(189−32, 189, 1539)-Net over F₄ — Constructive and digital

Digital (157, 189, 1539)-net over F₄, using

t-expansion [i] based on digital (156, 189, 1539)-net over F₄, using
- 3 times m-reduction [i] based on digital (156, 192, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 64, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(189−32, 189, 19403)-Net over F₄ — Digital

Digital (157, 189, 19403)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−32, 189, large)-Net in Base 4 — Upper bound on s

There is no (157, 189, large)-net in base 4, because

30 times m-reduction [i] would yield (157, 159, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]