MinT - Best Known (181, 181+75, s)-Nets in Base 4

Best Known (181, 181+75, s)-Nets in Base 4

(181, 181+75, 531)-Net over F₄ — Constructive and digital

Digital (181, 256, 531)-net over F₄, using

t-expansion [i] based on digital (179, 256, 531)-net over F₄, using
- 2 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]

(181, 181+75, 1132)-Net over F₄ — Digital

Digital (181, 256, 1132)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181, 181+75, 68854)-Net in Base 4 — Upper bound on s

There is no (181, 256, 68855)-net in base 4, because

1 times m-reduction [i] would yield (181, 255, 68855)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3353 039230 941431 862298 521196 808776 300873 077020 940672 873349 994361 599893 304323 431559 095941 163572 695722 021174 835413 944611 488341 259592 780604 883710 271476 878846 > 4²⁵⁵ [i]