MinT - Best Known (175−47, 175, s)-Nets in Base 3

Best Known (175−47, 175, s)-Nets in Base 3

(175−47, 175, 288)-Net over F₃ — Constructive and digital

Digital (128, 175, 288)-net over F₃, using

3¹ times duplication [i] based on digital (127, 174, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 58, 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]

(175−47, 175, 579)-Net over F₃ — Digital

Digital (128, 175, 579)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−47, 175, 19162)-Net in Base 3 — Upper bound on s

There is no (128, 175, 19163)-net in base 3, because

1 times m-reduction [i] would yield (128, 174, 19163)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104609 598401 370657 903999 473563 829141 799635 394136 034366 827040 076977 259090 121024 261059 > 3¹⁷⁴ [i]