MinT - Best Known (58, 58+21, s)-Nets in Base 3

Best Known (58, 58+21, s)-Nets in Base 3

(58, 58+21, 204)-Net over F₃ — Constructive and digital

Digital (58, 79, 204)-net over F₃, using

3¹ times duplication [i] based on digital (57, 78, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 26, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(58, 58+21, 328)-Net over F₃ — Digital

Digital (58, 79, 328)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+21, 11916)-Net in Base 3 — Upper bound on s

There is no (58, 79, 11917)-net in base 3, because

1 times m-reduction [i] would yield (58, 78, 11917)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 431071 782225 647132 422777 624547 770817 > 3⁷⁸ [i]