MinT - Best Known (241−65, 241, s)-Nets in Base 3

Best Known (241−65, 241, s)-Nets in Base 3

(241−65, 241, 288)-Net over F₃ — Constructive and digital

Digital (176, 241, 288)-net over F₃, using

t-expansion [i] based on digital (175, 241, 288)-net over F₃, using
- 5 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]

(241−65, 241, 747)-Net over F₃ — Digital

Digital (176, 241, 747)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−65, 241, 24193)-Net in Base 3 — Upper bound on s

There is no (176, 241, 24194)-net in base 3, because

1 times m-reduction [i] would yield (176, 240, 24194)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 232259 969343 703191 113043 148385 496563 072310 660001 896130 352128 987590 664084 235422 917125 965446 545115 582199 697555 220801 > 3²⁴⁰ [i]