MinT - Best Known (58, 58+24, s)-Nets in Base 3

Best Known (58, 58+24, s)-Nets in Base 3

(58, 58+24, 156)-Net over F₃ — Constructive and digital

Digital (58, 82, 156)-net over F₃, using

3¹ times duplication [i] based on digital (57, 81, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 27, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(58, 58+24, 241)-Net over F₃ — Digital

Digital (58, 82, 241)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+24, 4804)-Net in Base 3 — Upper bound on s

There is no (58, 82, 4805)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1332 874674 223696 466580 956275 524373 705009 > 3⁸² [i]