MinT - Best Known (140−45, 140, s)-Nets in Base 4

Best Known (140−45, 140, s)-Nets in Base 4

(140−45, 140, 240)-Net over F₄ — Constructive and digital

Digital (95, 140, 240)-net over F₄, using

1 times m-reduction [i] based on digital (95, 141, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 47, 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]

(140−45, 140, 468)-Net over F₄ — Digital

Digital (95, 140, 468)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−45, 140, 19197)-Net in Base 4 — Upper bound on s

There is no (95, 140, 19198)-net in base 4, because

1 times m-reduction [i] would yield (95, 139, 19198)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 485736 509269 925251 967299 267741 525062 453911 619002 118415 923300 529569 696920 648294 030428 > 4¹³⁹ [i]