MinT - Best Known (56, 79, s)-Nets in Base 3

Best Known (56, 79, s)-Nets in Base 3

(56, 79, 156)-Net over F₃ — Constructive and digital

Digital (56, 79, 156)-net over F₃, using

3¹ times duplication [i] based on digital (55, 78, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 26, 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]

(56, 79, 240)-Net over F₃ — Digital

Digital (56, 79, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 79, 5921)-Net in Base 3 — Upper bound on s

There is no (56, 79, 5922)-net in base 3, because

1 times m-reduction [i] would yield (56, 78, 5922)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 435509 729954 653701 772374 419735 041025 > 3⁷⁸ [i]