MinT - Best Known (226−63, 226, s)-Nets in Base 4

Best Known (226−63, 226, s)-Nets in Base 4

(226−63, 226, 531)-Net over F₄ — Constructive and digital

Digital (163, 226, 531)-net over F₄, using

8 times m-reduction [i] based on digital (163, 234, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 78, 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]

(226−63, 226, 1261)-Net over F₄ — Digital

Digital (163, 226, 1261)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−63, 226, 96959)-Net in Base 4 — Upper bound on s

There is no (163, 226, 96960)-net in base 4, because

1 times m-reduction [i] would yield (163, 225, 96960)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2908 203017 839819 904207 035554 583634 113519 055439 556545 280193 746508 321286 924161 266539 090419 732941 280265 497224 563907 444863 169705 971371 797621 > 4²²⁵ [i]