MinT - Best Known (200−53, 200, s)-Nets in Base 4

Best Known (200−53, 200, s)-Nets in Base 4

(200−53, 200, 531)-Net over F₄ — Constructive and digital

Digital (147, 200, 531)-net over F₄, using

10 times m-reduction [i] based on digital (147, 210, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 70, 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]

(200−53, 200, 576)-Net in Base 4 — Constructive

(147, 200, 576)-net in base 4, using

1 times m-reduction [i] based on (147, 201, 576)-net in base 4, using
- trace code for nets [i] based on (13, 67, 192)-net in base 64, using
  - 3 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]

(200−53, 200, 1420)-Net over F₄ — Digital

Digital (147, 200, 1420)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−53, 200, 142620)-Net in Base 4 — Upper bound on s

There is no (147, 200, 142621)-net in base 4, because

1 times m-reduction [i] would yield (147, 199, 142621)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 645623 902624 230879 918472 537994 585780 809147 082387 745053 606422 476508 216382 518118 607565 598299 919688 063787 178352 644378 639674 > 4¹⁹⁹ [i]