MinT - Best Known (225−44, 225, s)-Nets in Base 4

Best Known (225−44, 225, s)-Nets in Base 4

(225−44, 225, 1539)-Net over F₄ — Constructive and digital

Digital (181, 225, 1539)-net over F₄, using

t-expansion [i] based on digital (180, 225, 1539)-net over F₄, using
- 3 times m-reduction [i] based on digital (180, 228, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 76, 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]

(225−44, 225, 7977)-Net over F₄ — Digital

Digital (181, 225, 7977)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−44, 225, 4336723)-Net in Base 4 — Upper bound on s

There is no (181, 225, 4336724)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2907 364856 495408 082729 232502 133015 015110 735682 183666 137578 623851 257209 180604 025682 475913 696497 128079 220448 699253 079646 169096 091673 579760 > 4²²⁵ [i]