MinT - Best Known (182−50, 182, s)-Nets in Base 3

Best Known (182−50, 182, s)-Nets in Base 3

(182−50, 182, 282)-Net over F₃ — Constructive and digital

Digital (132, 182, 282)-net over F₃, using

1 times m-reduction [i] based on digital (132, 183, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 61, 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]

(182−50, 182, 551)-Net over F₃ — Digital

Digital (132, 182, 551)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−50, 182, 15112)-Net in Base 3 — Upper bound on s

There is no (132, 182, 15113)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 686 192922 481705 828909 464350 344628 825799 133137 467330 943535 101150 823512 157519 640220 737331 > 3¹⁸² [i]