MinT - Best Known (245−60, 245, s)-Nets in Base 3

Best Known (245−60, 245, s)-Nets in Base 3

(245−60, 245, 400)-Net over F₃ — Constructive and digital

Digital (185, 245, 400)-net over F₃, using

3¹ times duplication [i] based on digital (184, 244, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 61, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(245−60, 245, 1091)-Net over F₃ — Digital

Digital (185, 245, 1091)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−60, 245, 47421)-Net in Base 3 — Upper bound on s

There is no (185, 245, 47422)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 784 758553 496065 601322 405384 452061 410300 499774 460749 888110 129668 390504 680473 069811 165195 978133 589672 245912 134972 778965 > 3²⁴⁵ [i]