MinT - Best Known (206−89, 206, s)-Nets in Base 3

Best Known (206−89, 206, s)-Nets in Base 3

(206−89, 206, 128)-Net over F₃ — Constructive and digital

Digital (117, 206, 128)-net over F₃, using

2 times m-reduction [i] based on digital (117, 208, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 104, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(206−89, 206, 155)-Net over F₃ — Digital

Digital (117, 206, 155)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−89, 206, 1398)-Net in Base 3 — Upper bound on s

There is no (117, 206, 1399)-net in base 3, because

1 times m-reduction [i] would yield (117, 205, 1399)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65 264863 207525 561482 177977 559358 576295 576561 518162 600084 018320 559699 745078 679981 919825 808652 158889 > 3²⁰⁵ [i]