MinT - Best Known (159−43, 159, s)-Nets in Base 4

Best Known (159−43, 159, s)-Nets in Base 4

(159−43, 159, 531)-Net over F₄ — Constructive and digital

Digital (116, 159, 531)-net over F₄, using

t-expansion [i] based on digital (115, 159, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (115, 162, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 54, 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]

(159−43, 159, 1068)-Net over F₄ — Digital

Digital (116, 159, 1068)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−43, 159, 97967)-Net in Base 4 — Upper bound on s

There is no (116, 159, 97968)-net in base 4, because

1 times m-reduction [i] would yield (116, 158, 97968)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 133522 319330 363686 401350 961990 605396 028975 744627 324233 544731 708829 562095 378555 543402 937201 692010 > 4¹⁵⁸ [i]