MinT - Best Known (209−57, 209, s)-Nets in Base 4

Best Known (209−57, 209, s)-Nets in Base 4

(209−57, 209, 531)-Net over F₄ — Constructive and digital

Digital (152, 209, 531)-net over F₄, using

t-expansion [i] based on digital (151, 209, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 72, 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]

(209−57, 209, 1305)-Net over F₄ — Digital

Digital (152, 209, 1305)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−57, 209, 111748)-Net in Base 4 — Upper bound on s

There is no (152, 209, 111749)-net in base 4, because

1 times m-reduction [i] would yield (152, 208, 111749)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169262 441214 789908 507441 810753 612607 981164 966035 114398 735506 237210 862238 223245 801756 167522 212501 191675 798915 523439 271557 264112 > 4²⁰⁸ [i]