MinT - Best Known (175, 175+69, s)-Nets in Base 3

Best Known (175, 175+69, s)-Nets in Base 3

(175, 175+69, 288)-Net over F₃ — Constructive and digital

Digital (175, 244, 288)-net over F₃, using

2 times m-reduction [i] based on digital (175, 246, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 82, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(175, 175+69, 640)-Net over F₃ — Digital

Digital (175, 244, 640)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+69, 17362)-Net in Base 3 — Upper bound on s

There is no (175, 244, 17363)-net in base 3, because

1 times m-reduction [i] would yield (175, 243, 17363)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 203991 663147 381172 149269 583358 767031 250723 036115 146316 667503 879761 988528 861675 492510 747370 372513 706952 169984 006533 > 3²⁴³ [i]