MinT - Best Known (143−47, 143, s)-Nets in Base 4

Best Known (143−47, 143, s)-Nets in Base 4

(143−47, 143, 195)-Net over F₄ — Constructive and digital

Digital (96, 143, 195)-net over F₄, using

1 times m-reduction [i] based on digital (96, 144, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 48, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(143−47, 143, 208)-Net in Base 4 — Constructive

(96, 143, 208)-net in base 4, using

1 times m-reduction [i] based on (96, 144, 208)-net in base 4, using
- trace code for nets [i] based on (24, 72, 104)-net in base 16, using
  - 3 times m-reduction [i] based on (24, 75, 104)-net in base 16, using
    - base change [i] based on digital (9, 60, 104)-net over F₃₂, using
      - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(143−47, 143, 437)-Net over F₄ — Digital

Digital (96, 143, 437)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−47, 143, 16364)-Net in Base 4 — Upper bound on s

There is no (96, 143, 16365)-net in base 4, because

1 times m-reduction [i] would yield (96, 142, 16365)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 098884 376312 541471 633328 871842 980337 711253 337528 540133 146555 127638 419561 565559 682736 > 4¹⁴² [i]