MinT - Best Known (206−57, 206, s)-Nets in Base 4

Best Known (206−57, 206, s)-Nets in Base 4

(206−57, 206, 531)-Net over F₄ — Constructive and digital

Digital (149, 206, 531)-net over F₄, using

7 times m-reduction [i] based on digital (149, 213, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 71, 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]

(206−57, 206, 1207)-Net over F₄ — Digital

Digital (149, 206, 1207)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−57, 206, 96320)-Net in Base 4 — Upper bound on s

There is no (149, 206, 96321)-net in base 4, because

1 times m-reduction [i] would yield (149, 205, 96321)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2644 380004 194851 444847 897246 642747 102407 272758 435934 389974 773036 520965 465021 194636 287242 616539 021853 291494 475610 706034 685520 > 4²⁰⁵ [i]