MinT - Best Known (143, 143+58, s)-Nets in Base 3

Best Known (143, 143+58, s)-Nets in Base 3

(143, 143+58, 264)-Net over F₃ — Constructive and digital

Digital (143, 201, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 67, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(143, 143+58, 505)-Net over F₃ — Digital

Digital (143, 201, 505)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+58, 11802)-Net in Base 3 — Upper bound on s

There is no (143, 201, 11803)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 796993 875655 145933 089979 129727 208362 510472 807059 005617 593708 200965 135409 518289 077788 964558 497663 > 3²⁰¹ [i]