MinT - Best Known (115, 222, s)-Nets in Base 3

Best Known (115, 222, s)-Nets in Base 3

(115, 222, 76)-Net over F₃ — Constructive and digital

Digital (115, 222, 76)-net over F₃, using

3 times m-reduction [i] based on digital (115, 225, 76)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 70, 28)-net over F₃, using
    - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, 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]

(115, 222, 122)-Net over F₃ — Digital

Digital (115, 222, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 222, 953)-Net in Base 3 — Upper bound on s

There is no (115, 222, 954)-net in base 3, because

1 times m-reduction [i] would yield (115, 221, 954)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2801 354646 953741 529701 612677 891363 820515 450429 958068 487168 118268 326450 946711 078522 753214 229856 414268 735085 > 3²²¹ [i]