MinT - Best Known (207−86, 207, s)-Nets in Base 3

Best Known (207−86, 207, s)-Nets in Base 3

(207−86, 207, 148)-Net over F₃ — Constructive and digital

Digital (121, 207, 148)-net over F₃, using

1 times m-reduction [i] based on digital (121, 208, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 104, 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]

(207−86, 207, 173)-Net over F₃ — Digital

Digital (121, 207, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−86, 207, 1630)-Net in Base 3 — Upper bound on s

There is no (121, 207, 1631)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 594 414724 252994 128961 444381 863330 677557 096724 248499 005354 993970 299358 429736 420542 154335 848522 033451 > 3²⁰⁷ [i]