MinT - Best Known (102, 102+78, s)-Nets in Base 3

Best Known (102, 102+78, s)-Nets in Base 3

(102, 102+78, 80)-Net over F₃ — Constructive and digital

Digital (102, 180, 80)-net over F₃, using

8 times m-reduction [i] based on digital (102, 188, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 94, 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]

(102, 102+78, 137)-Net over F₃ — Digital

Digital (102, 180, 137)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+78, 1188)-Net in Base 3 — Upper bound on s

There is no (102, 180, 1189)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 78 628837 809275 013385 705483 188709 793199 994971 320850 885662 754951 079271 686734 417844 536027 > 3¹⁸⁰ [i]