MinT - Best Known (209−59, 209, s)-Nets in Base 4

Best Known (209−59, 209, s)-Nets in Base 4

(209−59, 209, 531)-Net over F₄ — Constructive and digital

Digital (150, 209, 531)-net over F₄, using

t-expansion [i] based on digital (149, 209, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (149, 213, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 71, 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]

(209−59, 209, 1117)-Net over F₄ — Digital

Digital (150, 209, 1117)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−59, 209, 80927)-Net in Base 4 — Upper bound on s

There is no (150, 209, 80928)-net in base 4, because

1 times m-reduction [i] would yield (150, 208, 80928)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169248 643498 238507 331641 541725 214255 752386 278388 105643 323778 801165 175099 494453 144086 208100 549658 344133 887578 941988 672981 912815 > 4²⁰⁸ [i]