MinT - Best Known (121, 221, s)-Nets in Base 3

Best Known (121, 221, s)-Nets in Base 3

(121, 221, 84)-Net over F₃ — Constructive and digital

Digital (121, 221, 84)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 76, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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, 145, 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, 221, 144)-Net over F₃ — Digital

Digital (121, 221, 144)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 221, 1203)-Net in Base 3 — Upper bound on s

There is no (121, 221, 1204)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2889 380352 636515 085194 589801 126568 021830 224953 378444 781504 841602 673990 327564 928158 200007 805298 522352 617817 > 3²²¹ [i]