MinT - Best Known (192−88, 192, s)-Nets in Base 3

Best Known (192−88, 192, s)-Nets in Base 3

(192−88, 192, 80)-Net over F₃ — Constructive and digital

Digital (104, 192, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 96, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(192−88, 192, 123)-Net over F₃ — Digital

Digital (104, 192, 123)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−88, 192, 999)-Net in Base 3 — Upper bound on s

There is no (104, 192, 1000)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41 766614 030551 677121 078131 373929 372657 626501 185964 220324 039247 832323 500923 447288 490820 220481 > 3¹⁹² [i]