MinT - Best Known (135, 135+61, s)-Nets in Base 3

Best Known (135, 135+61, s)-Nets in Base 3

(135, 135+61, 192)-Net over F₃ — Constructive and digital

Digital (135, 196, 192)-net over F₃, using

3¹ times duplication [i] based on digital (134, 195, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 65, 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]

(135, 135+61, 388)-Net over F₃ — Digital

Digital (135, 196, 388)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+61, 7574)-Net in Base 3 — Upper bound on s

There is no (135, 196, 7575)-net in base 3, because

1 times m-reduction [i] would yield (135, 195, 7575)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1094 656743 478378 483680 734823 105324 915414 169624 516278 054244 444579 183684 891007 741670 805879 737397 > 3¹⁹⁵ [i]