MinT - Best Known (211−56, 211, s)-Nets in Base 3

Best Known (211−56, 211, s)-Nets in Base 3

(211−56, 211, 288)-Net over F₃ — Constructive and digital

Digital (155, 211, 288)-net over F₃, using

5 times m-reduction [i] based on digital (155, 216, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 72, 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]

(211−56, 211, 707)-Net over F₃ — Digital

Digital (155, 211, 707)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−56, 211, 22227)-Net in Base 3 — Upper bound on s

There is no (155, 211, 22228)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47090 929340 073816 928391 330848 115356 257765 280784 781947 758257 406611 092691 227880 730843 634521 568401 832961 > 3²¹¹ [i]