MinT - Best Known (206−54, 206, s)-Nets in Base 4

Best Known (206−54, 206, s)-Nets in Base 4

(206−54, 206, 531)-Net over F₄ — Constructive and digital

Digital (152, 206, 531)-net over F₄, using

t-expansion [i] based on digital (151, 206, 531)-net over F₄, using
- 10 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 72, 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]

(206−54, 206, 576)-Net in Base 4 — Constructive

(152, 206, 576)-net in base 4, using

t-expansion [i] based on (151, 206, 576)-net in base 4, using
- 1 times m-reduction [i] based on (151, 207, 576)-net in base 4, using
  - trace code for nets [i] based on (13, 69, 192)-net in base 64, using
    - 1 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]

(206−54, 206, 1529)-Net over F₄ — Digital

Digital (152, 206, 1529)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−54, 206, 142795)-Net in Base 4 — Upper bound on s

There is no (152, 206, 142796)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10578 657298 391767 410825 473022 644875 063554 742356 476141 372023 391496 270023 586854 716244 545930 260004 785354 959021 504126 526821 773252 > 4²⁰⁶ [i]