MinT - Best Known (213−56, 213, s)-Nets in Base 3

Best Known (213−56, 213, s)-Nets in Base 3

(213−56, 213, 288)-Net over F₃ — Constructive and digital

Digital (157, 213, 288)-net over F₃, using

6 times m-reduction [i] based on digital (157, 219, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 73, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(213−56, 213, 738)-Net over F₃ — Digital

Digital (157, 213, 738)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−56, 213, 24044)-Net in Base 3 — Upper bound on s

There is no (157, 213, 24045)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423921 943331 409560 967105 180602 624613 147244 483860 110724 670740 337323 611021 578474 979266 198697 189427 453745 > 3²¹³ [i]