MinT - Best Known (139, 139+63, s)-Nets in Base 3

Best Known (139, 139+63, s)-Nets in Base 3

(139, 139+63, 192)-Net over F₃ — Constructive and digital

Digital (139, 202, 192)-net over F₃, using

3¹ times duplication [i] based on digital (138, 201, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 67, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(139, 139+63, 396)-Net over F₃ — Digital

Digital (139, 202, 396)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+63, 7671)-Net in Base 3 — Upper bound on s

There is no (139, 202, 7672)-net in base 3, because

1 times m-reduction [i] would yield (139, 201, 7672)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 798735 511343 702657 919011 731143 106551 380954 726850 499527 266976 971096 155666 877706 789055 210774 469025 > 3²⁰¹ [i]