MinT - Best Known (140, 140+55, s)-Nets in Base 4

Best Known (140, 140+55, s)-Nets in Base 4

(140, 140+55, 531)-Net over F₄ — Constructive and digital

Digital (140, 195, 531)-net over F₄, using

t-expansion [i] based on digital (139, 195, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (139, 198, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 66, 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]

(140, 140+55, 1059)-Net over F₄ — Digital

Digital (140, 195, 1059)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+55, 77103)-Net in Base 4 — Upper bound on s

There is no (140, 195, 77104)-net in base 4, because

1 times m-reduction [i] would yield (140, 194, 77104)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 630 539846 361257 114179 678222 900936 272263 963636 632425 933926 832102 496251 976322 284210 535015 466173 722096 089553 960231 772590 > 4¹⁹⁴ [i]