MinT - Best Known (55, 55+52, s)-Nets in Base 3

Best Known (55, 55+52, s)-Nets in Base 3

(55, 55+52, 52)-Net over F₃ — Constructive and digital

Digital (55, 107, 52)-net over F₃, using

2 times m-reduction [i] based on digital (55, 109, 52)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 40, 24)-net over F₃, using
    - net from sequence [i] based on digital (13, 23)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
  2. digital (15, 69, 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]

(55, 55+52, 65)-Net over F₃ — Digital

Digital (55, 107, 65)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+52, 460)-Net in Base 3 — Upper bound on s

There is no (55, 107, 461)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1182 191160 596092 510781 282972 499525 478174 374783 360897 > 3¹⁰⁷ [i]