MinT - Best Known (178−55, 178, s)-Nets in Base 3

Best Known (178−55, 178, s)-Nets in Base 3

(178−55, 178, 192)-Net over F₃ — Constructive and digital

Digital (123, 178, 192)-net over F₃, using

3¹ times duplication [i] based on digital (122, 177, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 59, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(178−55, 178, 365)-Net over F₃ — Digital

Digital (123, 178, 365)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−55, 178, 7304)-Net in Base 3 — Upper bound on s

There is no (123, 178, 7305)-net in base 3, because

1 times m-reduction [i] would yield (123, 177, 7305)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 824683 712827 975348 392045 021608 738280 367097 998189 312688 290188 463296 461478 002316 824347 > 3¹⁷⁷ [i]