MinT - Best Known (146, 198, s)-Nets in Base 4

Best Known (146, 198, s)-Nets in Base 4

(146, 198, 531)-Net over F₄ — Constructive and digital

Digital (146, 198, 531)-net over F₄, using

t-expansion [i] based on digital (145, 198, 531)-net over F₄, using
- 9 times m-reduction [i] based on digital (145, 207, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 69, 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]

(146, 198, 576)-Net in Base 4 — Constructive

(146, 198, 576)-net in base 4, using

t-expansion [i] based on (145, 198, 576)-net in base 4, using
- trace code for nets [i] based on (13, 66, 192)-net in base 64, using
  - 4 times m-reduction [i] based on (13, 70, 192)-net in base 64, using
    - base change [i] based on digital (3, 60, 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]

(146, 198, 1465)-Net over F₄ — Digital

Digital (146, 198, 1465)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 198, 135214)-Net in Base 4 — Upper bound on s

There is no (146, 198, 135215)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 161416 393970 826208 525259 295586 165400 093340 882136 026723 212100 543647 168965 504841 298559 682627 641137 819151 030513 312056 123898 > 4¹⁹⁸ [i]