MinT - Best Known (247−55, 247, s)-Nets in Base 3

Best Known (247−55, 247, s)-Nets in Base 3

(247−55, 247, 640)-Net over F₃ — Constructive and digital

Digital (192, 247, 640)-net over F₃, using

t-expansion [i] based on digital (191, 247, 640)-net over F₃, using
- 1 times m-reduction [i] based on digital (191, 248, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 62, 160)-net over F₈₁, using
    - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
        a function field by SÃ©mirat [i]

(247−55, 247, 1622)-Net over F₃ — Digital

Digital (192, 247, 1622)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−55, 247, 121447)-Net in Base 3 — Upper bound on s

There is no (192, 247, 121448)-net in base 3, because

1 times m-reduction [i] would yield (192, 246, 121448)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2354 643172 506101 866671 583297 039832 237028 418677 541860 718928 725442 998089 301995 616236 261935 195459 738148 700074 788646 346529 > 3²⁴⁶ [i]