MinT - Best Known (171, 171+62, s)-Nets in Base 4

Best Known (171, 171+62, s)-Nets in Base 4

(171, 171+62, 531)-Net over F₄ — Constructive and digital

Digital (171, 233, 531)-net over F₄, using

13 times m-reduction [i] based on digital (171, 246, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 82, 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]

(171, 171+62, 576)-Net in Base 4 — Constructive

(171, 233, 576)-net in base 4, using

4² times duplication [i] based on (169, 231, 576)-net in base 4, using
- t-expansion [i] based on (168, 231, 576)-net in base 4, using
  - trace code for nets [i] based on (14, 77, 192)-net in base 64, using
    - base change [i] based on digital (3, 66, 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]

(171, 171+62, 1596)-Net over F₄ — Digital

Digital (171, 233, 1596)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+62, 138673)-Net in Base 4 — Upper bound on s

There is no (171, 233, 138674)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 564735 770393 640559 639168 576279 302268 084484 583921 684232 532086 300216 950426 919461 601327 494525 384500 308699 848031 455632 668289 175423 247540 836816 > 4²³³ [i]