MinT - Best Known (136, 187, s)-Nets in Base 3

Best Known (136, 187, s)-Nets in Base 3

(136, 187, 288)-Net over F₃ — Constructive and digital

Digital (136, 187, 288)-net over F₃, using

3¹ times duplication [i] based on digital (135, 186, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 62, 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]

(136, 187, 579)-Net over F₃ — Digital

Digital (136, 187, 579)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 187, 18021)-Net in Base 3 — Upper bound on s

There is no (136, 187, 18022)-net in base 3, because

1 times m-reduction [i] would yield (136, 186, 18022)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55580 250210 147263 279048 232121 446587 265185 534736 007033 737585 131173 149059 354127 637309 433373 > 3¹⁸⁶ [i]