MinT - Best Known (144, 195, s)-Nets in Base 4

Best Known (144, 195, s)-Nets in Base 4

(144, 195, 531)-Net over F₄ — Constructive and digital

Digital (144, 195, 531)-net over F₄, using

t-expansion [i] based on digital (143, 195, 531)-net over F₄, using
- 9 times m-reduction [i] based on digital (143, 204, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 68, 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]

(144, 195, 576)-Net in Base 4 — Constructive

(144, 195, 576)-net in base 4, using

t-expansion [i] based on (143, 195, 576)-net in base 4, using
- trace code for nets [i] based on (13, 65, 192)-net in base 64, using
  - 5 times m-reduction [i] based on (13, 70, 192)-net in base 64, using
    - base change [i] based on digital (3, 60, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(144, 195, 1472)-Net over F₄ — Digital

Digital (144, 195, 1472)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 195, 159380)-Net in Base 4 — Upper bound on s

There is no (144, 195, 159381)-net in base 4, because

1 times m-reduction [i] would yield (144, 194, 159381)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 630 498947 281744 366580 862993 242652 887622 295912 404575 544655 139136 910215 374860 317010 364402 848250 713460 277240 505519 694464 > 4¹⁹⁴ [i]