MinT - Best Known (111, 111+95, s)-Nets in Base 3

Best Known (111, 111+95, s)-Nets in Base 3

(111, 111+95, 80)-Net over F₃ — Constructive and digital

Digital (111, 206, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 103, 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]

(111, 111+95, 129)-Net over F₃ — Digital

Digital (111, 206, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+95, 1061)-Net in Base 3 — Upper bound on s

There is no (111, 206, 1062)-net in base 3, because

1 times m-reduction [i] would yield (111, 205, 1062)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 66 628250 850200 859867 981163 836087 090990 401100 438845 971229 492901 664437 462064 505046 401922 108661 300233 > 3²⁰⁵ [i]