MinT - Best Known (173, 173+68, s)-Nets in Base 3

Best Known (173, 173+68, s)-Nets in Base 3

(173, 173+68, 288)-Net over F₃ — Constructive and digital

Digital (173, 241, 288)-net over F₃, using

2 times m-reduction [i] based on digital (173, 243, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 81, 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, 173+68, 638)-Net over F₃ — Digital

Digital (173, 241, 638)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173, 173+68, 16274)-Net in Base 3 — Upper bound on s

There is no (173, 241, 16275)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 702996 136851 658627 029190 791201 695104 609425 394029 919362 733614 078159 572306 759508 586186 891684 066233 846980 284730 514693 > 3²⁴¹ [i]