MinT - Best Known (252−73, 252, s)-Nets in Base 4

Best Known (252−73, 252, s)-Nets in Base 4

(252−73, 252, 531)-Net over F₄ — Constructive and digital

Digital (179, 252, 531)-net over F₄, using

6 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 86, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(252−73, 252, 1170)-Net over F₄ — Digital

Digital (179, 252, 1170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−73, 252, 75013)-Net in Base 4 — Upper bound on s

There is no (179, 252, 75014)-net in base 4, because

1 times m-reduction [i] would yield (179, 251, 75014)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 094834 561966 348426 468670 957102 309744 576383 291115 725658 875442 609021 796154 845746 021788 733528 581274 819841 088731 467431 227083 603993 144669 548877 918018 779896 > 4²⁵¹ [i]