MinT - Best Known (138−36, 138, s)-Nets in Base 3

Best Known (138−36, 138, s)-Nets in Base 3

(138−36, 138, 282)-Net over F₃ — Constructive and digital

Digital (102, 138, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 46, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(138−36, 138, 538)-Net over F₃ — Digital

Digital (102, 138, 538)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−36, 138, 17162)-Net in Base 3 — Upper bound on s

There is no (102, 138, 17163)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 696369 734069 191475 030078 667319 626293 796637 377276 597940 924363 666581 > 3¹³⁸ [i]