MinT - Best Known (200−78, 200, s)-Nets in Base 3

Best Known (200−78, 200, s)-Nets in Base 3

(200−78, 200, 156)-Net over F₃ — Constructive and digital

Digital (122, 200, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 100, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(200−78, 200, 201)-Net over F₃ — Digital

Digital (122, 200, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−78, 200, 2115)-Net in Base 3 — Upper bound on s

There is no (122, 200, 2116)-net in base 3, because

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]