MinT - Best Known (173−46, 173, s)-Nets in Base 3

Best Known (173−46, 173, s)-Nets in Base 3

(173−46, 173, 288)-Net over F₃ — Constructive and digital

Digital (127, 173, 288)-net over F₃, using

1 times m-reduction [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]

(173−46, 173, 596)-Net over F₃ — Digital

Digital (127, 173, 596)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−46, 173, 18267)-Net in Base 3 — Upper bound on s

There is no (127, 173, 18268)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34864 018427 436640 442849 450979 814341 984204 593800 463420 621823 599463 537062 968776 320913 > 3¹⁷³ [i]