MinT - Best Known (239−101, 239, s)-Nets in Base 3

Best Known (239−101, 239, s)-Nets in Base 3

(239−101, 239, 148)-Net over F₃ — Constructive and digital

Digital (138, 239, 148)-net over F₃, using

3 times m-reduction [i] based on digital (138, 242, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 121, 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]

(239−101, 239, 187)-Net over F₃ — Digital

Digital (138, 239, 187)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−101, 239, 1769)-Net in Base 3 — Upper bound on s

There is no (138, 239, 1770)-net in base 3, because

1 times m-reduction [i] would yield (138, 238, 1770)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 362592 565351 942243 519739 230439 258770 483602 709490 237438 083553 908271 359297 058635 445388 151663 399063 547469 143782 007589 > 3²³⁸ [i]