MinT - Best Known (224−43, 224, s)-Nets in Base 4

Best Known (224−43, 224, s)-Nets in Base 4

(224−43, 224, 1539)-Net over F₄ — Constructive and digital

Digital (181, 224, 1539)-net over F₄, using

t-expansion [i] based on digital (180, 224, 1539)-net over F₄, using
- 4 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]

(224−43, 224, 8967)-Net over F₄ — Digital

Digital (181, 224, 8967)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−43, 224, 7156060)-Net in Base 4 — Upper bound on s

There is no (181, 224, 7156061)-net in base 4, because

1 times m-reduction [i] would yield (181, 223, 7156061)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 181 709994 918837 452413 132442 525953 508464 265444 990372 378013 376783 172471 204636 974171 018514 420912 587996 025763 418055 336845 021780 195816 169404 > 4²²³ [i]