MinT - Best Known (257−54, 257, s)-Nets in Base 4

Best Known (257−54, 257, s)-Nets in Base 4

(257−54, 257, 1539)-Net over F₄ — Constructive and digital

Digital (203, 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]

(257−54, 257, 5729)-Net over F₄ — Digital

Digital (203, 257, 5729)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−54, 257, 1958843)-Net in Base 4 — Upper bound on s

There is no (203, 257, 1958844)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53631 352450 198979 335449 023790 293751 283222 644519 886117 803216 936790 100609 496359 376497 532025 978835 957396 739228 842815 780559 157755 849436 951292 623126 415993 878925 > 4²⁵⁷ [i]