MinT - Best Known (158, 158+61, s)-Nets in Base 4

Best Known (158, 158+61, s)-Nets in Base 4

(158, 158+61, 531)-Net over F₄ — Constructive and digital

Digital (158, 219, 531)-net over F₄, using

t-expansion [i] based on digital (157, 219, 531)-net over F₄, using
- 6 times m-reduction [i] based on digital (157, 225, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 75, 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, 158+61, 1232)-Net over F₄ — Digital

Digital (158, 219, 1232)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+61, 95175)-Net in Base 4 — Upper bound on s

There is no (158, 219, 95176)-net in base 4, because

1 times m-reduction [i] would yield (158, 218, 95176)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177481 918679 870036 038489 550276 972387 591780 222704 294443 815923 599492 084675 389506 001463 888803 614478 337346 720621 483693 732403 478980 671480 > 4²¹⁸ [i]