MinT - Best Known (113, 113+32, s)-Nets in Base 3

Best Known (113, 113+32, s)-Nets in Base 3

(113, 113+32, 600)-Net over F₃ — Constructive and digital

Digital (113, 145, 600)-net over F₃, using

3¹ times duplication [i] based on digital (112, 144, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 36, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(113, 113+32, 1074)-Net over F₃ — Digital

Digital (113, 145, 1074)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+32, 71668)-Net in Base 3 — Upper bound on s

There is no (113, 145, 71669)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1522 875384 466485 326012 462584 747242 340268 247948 330991 211704 031134 698945 > 3¹⁴⁵ [i]