MinT - Best Known (121, 121+108, s)-Nets in Base 3

Best Known (121, 121+108, s)-Nets in Base 3

(121, 121+108, 80)-Net over F₃ — Constructive and digital

Digital (121, 229, 80)-net over F₃, using

2 times m-reduction [i] based on digital (121, 231, 80)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 76, 32)-net over F₃, using
    - net from sequence [i] based on digital (21, 31)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
        an explicitly constructive algebraic function field [i]
  2. digital (45, 155, 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, 121+108, 133)-Net over F₃ — Digital

Digital (121, 229, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+108, 1053)-Net in Base 3 — Upper bound on s

There is no (121, 229, 1054)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 390875 754957 257526 194607 888512 920199 877632 465939 674119 413627 249966 733233 128707 867764 960519 023440 923975 642181 > 3²²⁹ [i]