MinT - Best Known (192−49, 192, s)-Nets in Base 3

Best Known (192−49, 192, s)-Nets in Base 3

(192−49, 192, 288)-Net over F₃ — Constructive and digital

Digital (143, 192, 288)-net over F₃, using

6 times m-reduction [i] based on digital (143, 198, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 66, 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]

(192−49, 192, 758)-Net over F₃ — Digital

Digital (143, 192, 758)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−49, 192, 30696)-Net in Base 3 — Upper bound on s

There is no (143, 192, 30697)-net in base 3, because

1 times m-reduction [i] would yield (143, 191, 30697)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 498651 763520 321577 569117 536094 121923 284245 922354 053145 304052 180432 162744 859522 329160 795617 > 3¹⁹¹ [i]