MinT - Best Known (174, 249, s)-Nets in Base 3

Best Known (174, 249, s)-Nets in Base 3

(174, 249, 252)-Net over F₃ — Constructive and digital

Digital (174, 249, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 83, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(174, 249, 530)-Net over F₃ — Digital

Digital (174, 249, 530)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 249, 11521)-Net in Base 3 — Upper bound on s

There is no (174, 249, 11522)-net in base 3, because

1 times m-reduction [i] would yield (174, 248, 11522)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21215 868463 553523 193793 680823 946350 036076 739601 256500 359359 550933 991601 115311 854011 462014 332726 057566 874460 061102 423773 > 3²⁴⁸ [i]