MinT - Best Known (176, 243, s)-Nets in Base 3

Best Known (176, 243, s)-Nets in Base 3

(176, 243, 288)-Net over F₃ — Constructive and digital

Digital (176, 243, 288)-net over F₃, using

t-expansion [i] based on digital (175, 243, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (175, 246, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 82, 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]

(176, 243, 696)-Net over F₃ — Digital

Digital (176, 243, 696)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 243, 20726)-Net in Base 3 — Upper bound on s

There is no (176, 243, 20727)-net in base 3, because

1 times m-reduction [i] would yield (176, 242, 20727)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 070121 614656 367374 709191 224696 806137 187910 281646 095031 138265 391276 185204 459950 350407 604786 315147 845974 397676 557743 > 3²⁴² [i]