MinT - Best Known (175−44, 175, s)-Nets in Base 3

Best Known (175−44, 175, s)-Nets in Base 3

(175−44, 175, 288)-Net over F₃ — Constructive and digital

Digital (131, 175, 288)-net over F₃, using

5 times m-reduction [i] based on digital (131, 180, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 60, 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]

(175−44, 175, 746)-Net over F₃ — Digital

Digital (131, 175, 746)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−44, 175, 28234)-Net in Base 3 — Upper bound on s

There is no (131, 175, 28235)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 313685 951584 017887 519791 430546 329570 146345 932537 300949 157632 202412 367351 844122 334797 > 3¹⁷⁵ [i]