MinT - Best Known (207−61, 207, s)-Nets in Base 4

Best Known (207−61, 207, s)-Nets in Base 4

(207−61, 207, 531)-Net over F₄ — Constructive and digital

Digital (146, 207, 531)-net over F₄, using

t-expansion [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]

(207−61, 207, 920)-Net over F₄ — Digital

Digital (146, 207, 920)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−61, 207, 54653)-Net in Base 4 — Upper bound on s

There is no (146, 207, 54654)-net in base 4, because

1 times m-reduction [i] would yield (146, 206, 54654)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10579 723601 848105 565695 025977 345249 958939 572250 166693 078316 942765 727655 941077 757809 852115 015209 727947 326589 624762 845142 084888 > 4²⁰⁶ [i]