MinT - Best Known (158−45, 158, s)-Nets in Base 4

Best Known (158−45, 158, s)-Nets in Base 4

(158−45, 158, 531)-Net over F₄ — Constructive and digital

Digital (113, 158, 531)-net over F₄, using

1 times m-reduction [i] based on digital (113, 159, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 53, 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]

(158−45, 158, 857)-Net over F₄ — Digital

Digital (113, 158, 857)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−45, 158, 59720)-Net in Base 4 — Upper bound on s

There is no (113, 158, 59721)-net in base 4, because

1 times m-reduction [i] would yield (113, 157, 59721)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33384 808753 023446 139439 391461 034700 520316 841490 535967 201432 703943 930266 444177 937512 441136 190736 > 4¹⁵⁷ [i]