MinT - Best Known (257−52, 257, s)-Nets in Base 4

Best Known (257−52, 257, s)-Nets in Base 4

(257−52, 257, 1539)-Net over F₄ — Constructive and digital

Digital (205, 257, 1539)-net over F₄, using

t-expansion [i] based on digital (200, 257, 1539)-net over F₄, using
- 1 times m-reduction [i] based on digital (200, 258, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(257−52, 257, 7181)-Net over F₄ — Digital

Digital (205, 257, 7181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−52, 257, 3142681)-Net in Base 4 — Upper bound on s

There is no (205, 257, 3142682)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53631 635071 976962 163105 992792 588135 598601 909544 945991 055673 017616 365569 352561 089261 508377 881246 386782 528301 778812 062940 093268 316603 411814 056413 315419 256840 > 4²⁵⁷ [i]