MinT - Best Known (182, 182+68, s)-Nets in Base 4

Best Known (182, 182+68, s)-Nets in Base 4

(182, 182+68, 531)-Net over F₄ — Constructive and digital

Digital (182, 250, 531)-net over F₄, using

t-expansion [i] based on digital (179, 250, 531)-net over F₄, using
- 8 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(182, 182+68, 576)-Net in Base 4 — Constructive

(182, 250, 576)-net in base 4, using

4¹ times duplication [i] based on (181, 249, 576)-net in base 4, using
- trace code for nets [i] based on (15, 83, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
    - base change [i] based on digital (3, 72, 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]

(182, 182+68, 1533)-Net over F₄ — Digital

Digital (182, 250, 1533)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182, 182+68, 120549)-Net in Base 4 — Upper bound on s

There is no (182, 250, 120550)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 273798 383094 434719 754340 794688 172080 429089 820225 629080 372140 593086 588811 655368 567143 177752 525259 323841 388594 736381 838311 560873 795779 308791 466610 573702 > 4²⁵⁰ [i]