MinT - Best Known (116, 116+97, s)-Nets in Base 3

Best Known (116, 116+97, s)-Nets in Base 3

(116, 116+97, 80)-Net over F₃ — Constructive and digital

Digital (116, 213, 80)-net over F₃, using

3 times m-reduction [i] based on digital (116, 216, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 108, 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]

(116, 116+97, 137)-Net over F₃ — Digital

Digital (116, 213, 137)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+97, 1152)-Net in Base 3 — Upper bound on s

There is no (116, 213, 1153)-net in base 3, because

1 times m-reduction [i] would yield (116, 212, 1153)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141768 013975 969661 031822 971245 686919 995891 987068 906454 717956 481062 148201 612615 831632 077801 021151 712705 > 3²¹² [i]