MinT - Best Known (257−56, 257, s)-Nets in Base 4

Best Known (257−56, 257, s)-Nets in Base 4

(257−56, 257, 1539)-Net over F₄ — Constructive and digital

Digital (201, 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]

(257−56, 257, 4654)-Net over F₄ — Digital

Digital (201, 257, 4654)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−56, 257, 1264522)-Net in Base 4 — Upper bound on s

There is no (201, 257, 1264523)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53631 804090 666988 884357 509998 137852 992738 249373 500641 852116 877143 352243 784536 794692 906221 044884 401884 730239 734218 031089 134064 343047 009493 713493 731566 617440 > 4²⁵⁷ [i]