MinT - Best Known (103, 103+42, s)-Nets in Base 3

Best Known (103, 103+42, s)-Nets in Base 3

(103, 103+42, 228)-Net over F₃ — Constructive and digital

Digital (103, 145, 228)-net over F₃, using

3¹ times duplication [i] based on digital (102, 144, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 48, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(103, 103+42, 380)-Net over F₃ — Digital

Digital (103, 145, 380)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+42, 8527)-Net in Base 3 — Upper bound on s

There is no (103, 145, 8528)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1523 885436 036560 237628 391996 304768 869135 396422 934965 729226 392970 108577 > 3¹⁴⁵ [i]