MinT - Best Known (182, 234, s)-Nets in Base 3

Best Known (182, 234, s)-Nets in Base 3

(182, 234, 640)-Net over F₃ — Constructive and digital

Digital (182, 234, 640)-net over F₃, using

2 times m-reduction [i] based on digital (182, 236, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 59, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(182, 234, 1560)-Net over F₃ — Digital

Digital (182, 234, 1560)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182, 234, 103812)-Net in Base 3 — Upper bound on s

There is no (182, 234, 103813)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4430 769210 160264 478648 280214 508528 724425 494302 497420 635157 371003 942828 799032 341846 432552 795918 257388 318637 472049 > 3²³⁴ [i]