MinT - Best Known (252−74, 252, s)-Nets in Base 4

Best Known (252−74, 252, s)-Nets in Base 4

(252−74, 252, 531)-Net over F₄ — Constructive and digital

Digital (178, 252, 531)-net over F₄, using

t-expansion [i] based on digital (177, 252, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (177, 255, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 85, 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]

(252−74, 252, 1105)-Net over F₄ — Digital

Digital (178, 252, 1105)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−74, 252, 61530)-Net in Base 4 — Upper bound on s

There is no (178, 252, 61531)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 377492 318145 203483 040134 313068 247361 308079 131402 188108 263646 458691 772481 893415 721192 786951 119990 821842 079257 528648 079793 369527 869164 752249 596809 564200 > 4²⁵² [i]