MinT - Best Known (176−46, 176, s)-Nets in Base 4

Best Known (176−46, 176, s)-Nets in Base 4

(176−46, 176, 531)-Net over F₄ — Constructive and digital

Digital (130, 176, 531)-net over F₄, using

t-expansion [i] based on digital (129, 176, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (129, 183, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 61, 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]

(176−46, 176, 576)-Net in Base 4 — Constructive

(130, 176, 576)-net in base 4, using

1 times m-reduction [i] based on (130, 177, 576)-net in base 4, using
- trace code for nets [i] based on (12, 59, 192)-net in base 64, using
  - 4 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
    - base change [i] based on digital (3, 54, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(176−46, 176, 1352)-Net over F₄ — Digital

Digital (130, 176, 1352)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−46, 176, 127156)-Net in Base 4 — Upper bound on s

There is no (130, 176, 127157)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9174 594413 948937 601998 599195 155176 145299 823817 794978 409328 381537 943725 259709 202988 090373 459066 723728 242592 > 4¹⁷⁶ [i]