MinT - Best Known (188−54, 188, s)-Nets in Base 4

Best Known (188−54, 188, s)-Nets in Base 4

(188−54, 188, 531)-Net over F₄ — Constructive and digital

Digital (134, 188, 531)-net over F₄, using

t-expansion [i] based on digital (133, 188, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (133, 189, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 63, 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]

(188−54, 188, 948)-Net over F₄ — Digital

Digital (134, 188, 948)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−54, 188, 56655)-Net in Base 4 — Upper bound on s

There is no (134, 188, 56656)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 153986 398610 411236 229821 372131 217625 216006 177096 937190 285714 130939 525992 435340 631853 234530 972374 471113 299983 298892 > 4¹⁸⁸ [i]