MinT - Best Known (135, 135+47, s)-Nets in Base 3

Best Known (135, 135+47, s)-Nets in Base 3

(135, 135+47, 288)-Net over F₃ — Constructive and digital

Digital (135, 182, 288)-net over F₃, using

4 times m-reduction [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]

(135, 135+47, 693)-Net over F₃ — Digital

Digital (135, 182, 693)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+47, 26779)-Net in Base 3 — Upper bound on s

There is no (135, 182, 26780)-net in base 3, because

1 times m-reduction [i] would yield (135, 181, 26780)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 678079 699570 614892 867625 485905 247318 645282 467356 319174 793728 771609 852509 565088 841361 > 3¹⁸¹ [i]