MinT - Best Known (141−61, 141, s)-Nets in Base 3

Best Known (141−61, 141, s)-Nets in Base 3

(141−61, 141, 80)-Net over F₃ — Constructive and digital

Digital (80, 141, 80)-net over F₃, using

3 times m-reduction [i] based on digital (80, 144, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 72, 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]

(141−61, 141, 111)-Net over F₃ — Digital

Digital (80, 141, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−61, 141, 985)-Net in Base 3 — Upper bound on s

There is no (80, 141, 986)-net in base 3, because

1 times m-reduction [i] would yield (80, 140, 986)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 354975 145541 664084 275997 823298 786835 151082 291178 576283 582633 847997 > 3¹⁴⁰ [i]