MinT - Best Known (140−42, 140, s)-Nets in Base 4

Best Known (140−42, 140, s)-Nets in Base 4

(140−42, 140, 312)-Net over F₄ — Constructive and digital

Digital (98, 140, 312)-net over F₄, using

t-expansion [i] based on digital (97, 140, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (97, 141, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 47, 104)-net over F₆₄, using
    - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(140−42, 140, 622)-Net over F₄ — Digital

Digital (98, 140, 622)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−42, 140, 29844)-Net in Base 4 — Upper bound on s

There is no (98, 140, 29845)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 944007 828342 498873 346973 700787 765422 633146 457325 754466 747771 658882 978183 753806 237684 > 4¹⁴⁰ [i]