MinT - Best Known (201−55, 201, s)-Nets in Base 4

Best Known (201−55, 201, s)-Nets in Base 4

(201−55, 201, 531)-Net over F₄ — Constructive and digital

Digital (146, 201, 531)-net over F₄, using

t-expansion [i] based on digital (145, 201, 531)-net over F₄, using
- 6 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]

(201−55, 201, 1244)-Net over F₄ — Digital

Digital (146, 201, 1244)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(201−55, 201, 104929)-Net in Base 4 — Upper bound on s

There is no (146, 201, 104930)-net in base 4, because

1 times m-reduction [i] would yield (146, 200, 104930)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 582499 836231 884598 017829 644680 113750 519298 732643 165951 557863 416825 288191 529803 082192 985382 999959 415204 277162 358898 302320 > 4²⁰⁰ [i]