MinT - Best Known (140, 140+102, s)-Nets in Base 3

Best Known (140, 140+102, s)-Nets in Base 3

(140, 140+102, 148)-Net over F₃ — Constructive and digital

Digital (140, 242, 148)-net over F₃, using

4 times m-reduction [i] based on digital (140, 246, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 123, 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]

(140, 140+102, 191)-Net over F₃ — Digital

Digital (140, 242, 191)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+102, 1773)-Net in Base 3 — Upper bound on s

There is no (140, 242, 1774)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 733506 277094 876462 554405 240096 554746 533539 682112 135365 186774 926357 661095 603389 302724 618893 273319 591279 417751 550561 > 3²⁴² [i]