MinT - Best Known (157−43, 157, s)-Nets in Base 4

Best Known (157−43, 157, s)-Nets in Base 4

(157−43, 157, 531)-Net over F₄ — Constructive and digital

Digital (114, 157, 531)-net over F₄, using

t-expansion [i] based on digital (113, 157, 531)-net over F₄, using
- 2 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]

(157−43, 157, 1001)-Net over F₄ — Digital

Digital (114, 157, 1001)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−43, 157, 85848)-Net in Base 4 — Upper bound on s

There is no (114, 157, 85849)-net in base 4, because

1 times m-reduction [i] would yield (114, 156, 85849)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8345 419524 459251 006988 745904 522046 321489 542139 448111 912495 305470 046746 885579 406576 916660 344928 > 4¹⁵⁶ [i]