MinT - Best Known (121, 217, s)-Nets in Base 3

Best Known (121, 217, s)-Nets in Base 3

(121, 217, 85)-Net over F₃ — Constructive and digital

Digital (121, 217, 85)-net over F₃, using

2 times m-reduction [i] based on digital (121, 219, 85)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 76, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
  2. digital (45, 143, 48)-net over F₃, using
    - net from sequence [i] based on digital (45, 47)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
        an explicitly constructive algebraic function field [i]

(121, 217, 151)-Net over F₃ — Digital

Digital (121, 217, 151)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 217, 1298)-Net in Base 3 — Upper bound on s

There is no (121, 217, 1299)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35 221824 153490 088030 991571 604963 769472 707620 770546 292411 023235 685444 026505 706514 060043 936494 351372 376225 > 3²¹⁷ [i]