MinT - Best Known (184, 233, s)-Nets in Base 4

Best Known (184, 233, s)-Nets in Base 4

(184, 233, 1539)-Net over F₄ — Constructive and digital

Digital (184, 233, 1539)-net over F₄, using

1 times m-reduction [i] based on digital (184, 234, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 78, 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]

(184, 233, 5250)-Net over F₄ — Digital

Digital (184, 233, 5250)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(184, 233, 2158493)-Net in Base 4 — Upper bound on s

There is no (184, 233, 2158494)-net in base 4, because

1 times m-reduction [i] would yield (184, 232, 2158494)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 634203 076150 801898 087280 718079 180550 703115 445869 116206 223545 711934 854648 748327 874406 398338 073764 327400 788646 745785 758914 739603 637553 676811 > 4²³² [i]