MinT - Best Known (143, 143+56, s)-Nets in Base 3

Best Known (143, 143+56, s)-Nets in Base 3

(143, 143+56, 282)-Net over F₃ — Constructive and digital

Digital (143, 199, 282)-net over F₃, using

3¹ times duplication [i] based on digital (142, 198, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 66, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(143, 143+56, 546)-Net over F₃ — Digital

Digital (143, 199, 546)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+56, 13870)-Net in Base 3 — Upper bound on s

There is no (143, 199, 13871)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88670 928779 515985 495743 358633 795406 090467 792180 969777 340350 185304 161243 881633 782395 554162 894537 > 3¹⁹⁹ [i]