MinT - Best Known (137, 137+51, s)-Nets in Base 4

Best Known (137, 137+51, s)-Nets in Base 4

(137, 137+51, 531)-Net over F₄ — Constructive and digital

Digital (137, 188, 531)-net over F₄, using

7 times m-reduction [i] based on digital (137, 195, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 65, 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]

(137, 137+51, 1217)-Net over F₄ — Digital

Digital (137, 188, 1217)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+51, 108101)-Net in Base 4 — Upper bound on s

There is no (137, 188, 108102)-net in base 4, because

1 times m-reduction [i] would yield (137, 187, 108102)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38483 164448 587771 343008 063647 725778 246729 218213 313003 158845 695895 472594 397870 614354 491295 233862 350635 994287 902056 > 4¹⁸⁷ [i]