MinT - Best Known (207−57, 207, s)-Nets in Base 4

Best Known (207−57, 207, s)-Nets in Base 4

(207−57, 207, 531)-Net over F₄ — Constructive and digital

Digital (150, 207, 531)-net over F₄, using

t-expansion [i] based on digital (149, 207, 531)-net over F₄, using
- 6 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]

(207−57, 207, 1239)-Net over F₄ — Digital

Digital (150, 207, 1239)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−57, 207, 101210)-Net in Base 4 — Upper bound on s

There is no (150, 207, 101211)-net in base 4, because

1 times m-reduction [i] would yield (150, 206, 101211)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10577 259849 467348 943065 066875 572763 673304 181365 213166 767374 947152 667038 236949 155564 686322 990869 615453 371863 204237 948496 033232 > 4²⁰⁶ [i]