MinT - Best Known (136, 136+98, s)-Nets in Base 3

Best Known (136, 136+98, s)-Nets in Base 3

(136, 136+98, 148)-Net over F₃ — Constructive and digital

Digital (136, 234, 148)-net over F₃, using

4 times m-reduction [i] based on digital (136, 238, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 119, 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]

(136, 136+98, 189)-Net over F₃ — Digital

Digital (136, 234, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+98, 1766)-Net in Base 3 — Upper bound on s

There is no (136, 234, 1767)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4476 454840 196963 759555 823518 851757 948730 283535 453412 787451 796485 581142 989679 877581 644877 357271 066320 840953 397103 > 3²³⁴ [i]