MinT - Best Known (164, 164+63, s)-Nets in Base 4

Best Known (164, 164+63, s)-Nets in Base 4

(164, 164+63, 531)-Net over F₄ — Constructive and digital

Digital (164, 227, 531)-net over F₄, using

t-expansion [i] based on digital (163, 227, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (163, 234, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 78, 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]

(164, 164+63, 1291)-Net over F₄ — Digital

Digital (164, 227, 1291)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+63, 101394)-Net in Base 4 — Upper bound on s

There is no (164, 227, 101395)-net in base 4, because

1 times m-reduction [i] would yield (164, 226, 101395)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11630 887258 227620 570962 571131 560737 186338 368320 784220 321463 967139 292705 466481 201451 482875 181872 501008 487802 869665 659688 430193 939752 681472 > 4²²⁶ [i]