MinT - Best Known (207−85, 207, s)-Nets in Base 3

Best Known (207−85, 207, s)-Nets in Base 3

(207−85, 207, 148)-Net over F₃ — Constructive and digital

Digital (122, 207, 148)-net over F₃, using

3 times m-reduction [i] based on digital (122, 210, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 105, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(207−85, 207, 179)-Net over F₃ — Digital

Digital (122, 207, 179)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−85, 207, 1765)-Net in Base 3 — Upper bound on s

There is no (122, 207, 1766)-net in base 3, because

1 times m-reduction [i] would yield (122, 206, 1766)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 194 493799 419588 862216 514559 695672 162134 615592 695010 672842 122950 205505 977480 692579 742321 748832 108925 > 3²⁰⁶ [i]