MinT - Best Known (209−61, 209, s)-Nets in Base 4

Best Known (209−61, 209, s)-Nets in Base 4

(209−61, 209, 531)-Net over F₄ — Constructive and digital

Digital (148, 209, 531)-net over F₄, using

t-expansion [i] based on digital (147, 209, 531)-net over F₄, using
- 1 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]

(209−61, 209, 966)-Net over F₄ — Digital

Digital (148, 209, 966)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−61, 209, 59947)-Net in Base 4 — Upper bound on s

There is no (148, 209, 59948)-net in base 4, because

1 times m-reduction [i] would yield (148, 208, 59948)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169254 928744 360761 027534 109501 894984 111329 640055 272923 399002 220187 723141 699075 386006 493467 895521 402013 513349 002006 616330 388520 > 4²⁰⁸ [i]