MinT - Best Known (112, 204, s)-Nets in Base 3

Best Known (112, 204, s)-Nets in Base 3

(112, 204, 80)-Net over F₃ — Constructive and digital

Digital (112, 204, 80)-net over F₃, using

4 times m-reduction [i] based on digital (112, 208, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 104, 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]

(112, 204, 136)-Net over F₃ — Digital

Digital (112, 204, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 204, 1130)-Net in Base 3 — Upper bound on s

There is no (112, 204, 1131)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 969563 790894 121339 188335 708235 036721 686876 865143 378301 473487 815691 220517 830104 259589 773652 965533 > 3²⁰⁴ [i]