MinT - Best Known (110, 110+86, s)-Nets in Base 3

Best Known (110, 110+86, s)-Nets in Base 3

(110, 110+86, 80)-Net over F₃ — Constructive and digital

Digital (110, 196, 80)-net over F₃, using

8 times m-reduction [i] based on digital (110, 204, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 102, 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]

(110, 110+86, 142)-Net over F₃ — Digital

Digital (110, 196, 142)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 110+86, 1220)-Net in Base 3 — Upper bound on s

There is no (110, 196, 1221)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3328 247796 759991 074447 317804 481181 412881 444036 322609 528363 484087 989934 533421 675979 971679 764363 > 3¹⁹⁶ [i]