MinT - Best Known (114−40, 114, s)-Nets in Base 3

Best Known (114−40, 114, s)-Nets in Base 3

(114−40, 114, 148)-Net over F₃ — Constructive and digital

Digital (74, 114, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 57, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(114−40, 114, 172)-Net over F₃ — Digital

Digital (74, 114, 172)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−40, 114, 2157)-Net in Base 3 — Upper bound on s

There is no (74, 114, 2158)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 473708 284835 623304 511368 079419 821369 664448 197238 390697 > 3¹¹⁴ [i]