MinT - Best Known (141, 141+59, s)-Nets in Base 3

Best Known (141, 141+59, s)-Nets in Base 3

(141, 141+59, 246)-Net over F₃ — Constructive and digital

Digital (141, 200, 246)-net over F₃, using

1 times m-reduction [i] based on digital (141, 201, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 67, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(141, 141+59, 468)-Net over F₃ — Digital

Digital (141, 200, 468)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+59, 10939)-Net in Base 3 — Upper bound on s

There is no (141, 200, 10940)-net in base 3, because

1 times m-reduction [i] would yield (141, 199, 10940)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88626 890691 884344 764410 506788 358170 814213 653763 872466 770206 848022 198770 322517 346287 008408 247897 > 3¹⁹⁹ [i]