MinT - Best Known (142, 142+63, s)-Nets in Base 3

Best Known (142, 142+63, s)-Nets in Base 3

(142, 142+63, 204)-Net over F₃ — Constructive and digital

Digital (142, 205, 204)-net over F₃, using

3¹ times duplication [i] based on digital (141, 204, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 68, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(142, 142+63, 419)-Net over F₃ — Digital

Digital (142, 205, 419)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+63, 8535)-Net in Base 3 — Upper bound on s

There is no (142, 205, 8536)-net in base 3, because

1 times m-reduction [i] would yield (142, 204, 8536)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 564674 949283 345396 090410 300373 587612 496039 747797 906048 466768 836348 070323 601555 476568 952522 015265 > 3²⁰⁴ [i]