MinT - Best Known (139, 139+49, s)-Nets in Base 3

Best Known (139, 139+49, s)-Nets in Base 3

(139, 139+49, 288)-Net over F₃ — Constructive and digital

Digital (139, 188, 288)-net over F₃, using

4 times m-reduction [i] based on digital (139, 192, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 64, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(139, 139+49, 687)-Net over F₃ — Digital

Digital (139, 188, 687)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+49, 25556)-Net in Base 3 — Upper bound on s

There is no (139, 188, 25557)-net in base 3, because

1 times m-reduction [i] would yield (139, 187, 25557)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 166658 414152 461914 814588 338015 233470 436659 748893 940843 781544 059504 613020 708386 610289 590049 > 3¹⁸⁷ [i]