MinT - Best Known (192, 192+54, s)-Nets in Base 3

Best Known (192, 192+54, s)-Nets in Base 3

(192, 192+54, 688)-Net over F₃ — Constructive and digital

Digital (192, 246, 688)-net over F₃, using

3² times duplication [i] based on digital (190, 244, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 61, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(192, 192+54, 1714)-Net over F₃ — Digital

Digital (192, 246, 1714)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192, 192+54, 121447)-Net in Base 3 — Upper bound on s

There is no (192, 246, 121448)-net in base 3, because

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]