MinT - Best Known (128, 128+51, s)-Nets in Base 4

Best Known (128, 128+51, s)-Nets in Base 4

(128, 128+51, 531)-Net over F₄ — Constructive and digital

Digital (128, 179, 531)-net over F₄, using

t-expansion [i] based on digital (127, 179, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (127, 180, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 60, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(128, 128+51, 944)-Net over F₄ — Digital

Digital (128, 179, 944)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+51, 65620)-Net in Base 4 — Upper bound on s

There is no (128, 179, 65621)-net in base 4, because

1 times m-reduction [i] would yield (128, 178, 65621)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 146831 805349 516222 802744 866200 599822 770515 477841 744487 034796 615938 586842 164223 299834 881096 131682 555631 123776 > 4¹⁷⁸ [i]