MinT - Best Known (135, 135+49, s)-Nets in Base 3

Best Known (135, 135+49, s)-Nets in Base 3

(135, 135+49, 288)-Net over F₃ — Constructive and digital

Digital (135, 184, 288)-net over F₃, using

2 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+49, 623)-Net over F₃ — Digital

Digital (135, 184, 623)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+49, 21276)-Net in Base 3 — Upper bound on s

There is no (135, 184, 21277)-net in base 3, because

1 times m-reduction [i] would yield (135, 183, 21277)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2057 614803 858338 277841 105638 631665 498071 279593 145010 715655 842546 240848 607634 094449 666337 > 3¹⁸³ [i]