MinT - Best Known (199−65, 199, s)-Nets in Base 4

Best Known (199−65, 199, s)-Nets in Base 4

(199−65, 199, 240)-Net over F₄ — Constructive and digital

Digital (134, 199, 240)-net over F₄, using

4¹ times duplication [i] based on digital (133, 198, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 66, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(199−65, 199, 590)-Net over F₄ — Digital

Digital (134, 199, 590)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−65, 199, 22620)-Net in Base 4 — Upper bound on s

There is no (134, 199, 22621)-net in base 4, because

1 times m-reduction [i] would yield (134, 198, 22621)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 161489 882446 653792 679338 327428 372050 302701 155867 305006 130850 141135 121742 226908 056637 154995 387560 632629 005218 159141 874346 > 4¹⁹⁸ [i]