MinT - Best Known (197−89, 197, s)-Nets in Base 3

Best Known (197−89, 197, s)-Nets in Base 3

(197−89, 197, 80)-Net over F₃ — Constructive and digital

Digital (108, 197, 80)-net over F₃, using

3 times m-reduction [i] based on digital (108, 200, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 100, 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]

(197−89, 197, 131)-Net over F₃ — Digital

Digital (108, 197, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−89, 197, 1108)-Net in Base 3 — Upper bound on s

There is no (108, 197, 1109)-net in base 3, because

1 times m-reduction [i] would yield (108, 196, 1109)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3324 941007 031460 310621 426692 416979 292450 314213 543069 022639 105965 289981 743402 119288 186673 214513 > 3¹⁹⁶ [i]