MinT - Best Known (188−53, 188, s)-Nets in Base 4

Best Known (188−53, 188, s)-Nets in Base 4

(188−53, 188, 531)-Net over F₄ — Constructive and digital

Digital (135, 188, 531)-net over F₄, using

4 times m-reduction [i] based on digital (135, 192, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 64, 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]

(188−53, 188, 1030)-Net over F₄ — Digital

Digital (135, 188, 1030)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−53, 188, 75205)-Net in Base 4 — Upper bound on s

There is no (135, 188, 75206)-net in base 4, because

1 times m-reduction [i] would yield (135, 187, 75206)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38483 590204 989402 349194 647394 823111 703315 054342 325795 066360 680426 681100 960306 943531 636478 857930 695638 149047 909232 > 4¹⁸⁷ [i]