MinT - Best Known (142, 142+59, s)-Nets in Base 3

Best Known (142, 142+59, s)-Nets in Base 3

(142, 142+59, 252)-Net over F₃ — Constructive and digital

Digital (142, 201, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 67, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(142, 142+59, 478)-Net over F₃ — Digital

Digital (142, 201, 478)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+59, 11363)-Net in Base 3 — Upper bound on s

There is no (142, 201, 11364)-net in base 3, because

1 times m-reduction [i] would yield (142, 200, 11364)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 266225 858566 953594 276728 644955 139738 913848 328545 637356 038583 751650 247149 311887 946632 720844 626473 > 3²⁰⁰ [i]