MinT - Best Known (221−63, 221, s)-Nets in Base 4

Best Known (221−63, 221, s)-Nets in Base 4

(221−63, 221, 531)-Net over F₄ — Constructive and digital

Digital (158, 221, 531)-net over F₄, using

t-expansion [i] based on digital (157, 221, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (157, 225, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 75, 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]

(221−63, 221, 1121)-Net over F₄ — Digital

Digital (158, 221, 1121)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−63, 221, 77527)-Net in Base 4 — Upper bound on s

There is no (158, 221, 77528)-net in base 4, because

1 times m-reduction [i] would yield (158, 220, 77528)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 840214 339037 724170 273655 443010 739769 770316 849639 949122 209249 717516 853664 640751 211013 714565 843719 872415 166218 884597 551874 574927 716440 > 4²²⁰ [i]