MinT - Best Known (122, 201, s)-Nets in Base 3

Best Known (122, 201, s)-Nets in Base 3

(122, 201, 148)-Net over F₃ — Constructive and digital

Digital (122, 201, 148)-net over F₃, using

9 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]

(122, 201, 197)-Net over F₃ — Digital

Digital (122, 201, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 201, 2115)-Net in Base 3 — Upper bound on s

There is no (122, 201, 2116)-net in base 3, because

1 times m-reduction [i] would yield (122, 200, 2116)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 268448 899107 540915 340867 934073 176501 135734 797128 403106 525799 577910 209874 155626 545073 526242 929137 > 3²⁰⁰ [i]