MinT - Best Known (109, 160, s)-Nets in Base 4

Best Known (109, 160, s)-Nets in Base 4

(109, 160, 240)-Net over F₄ — Constructive and digital

Digital (109, 160, 240)-net over F₄, using

2 times m-reduction [i] based on digital (109, 162, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 54, 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]

(109, 160, 539)-Net over F₄ — Digital

Digital (109, 160, 539)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 160, 22867)-Net in Base 4 — Upper bound on s

There is no (109, 160, 22868)-net in base 4, because

1 times m-reduction [i] would yield (109, 159, 22868)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534240 281250 643335 181662 478867 760719 657991 282176 058097 400255 058085 162100 826238 735822 920831 661256 > 4¹⁵⁹ [i]