MinT - Best Known (100−38, 100, s)-Nets in Base 3

Best Known (100−38, 100, s)-Nets in Base 3

(100−38, 100, 80)-Net over F₃ — Constructive and digital

Digital (62, 100, 80)-net over F₃, using

8 times m-reduction [i] based on digital (62, 108, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 54, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(100−38, 100, 122)-Net over F₃ — Digital

Digital (62, 100, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−38, 100, 1267)-Net in Base 3 — Upper bound on s

There is no (62, 100, 1268)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 515884 638089 188529 413400 166818 801929 661376 694385 > 3¹⁰⁰ [i]