MinT - Best Known (243−69, 243, s)-Nets in Base 3

Best Known (243−69, 243, s)-Nets in Base 3

(243−69, 243, 288)-Net over F₃ — Constructive and digital

Digital (174, 243, 288)-net over F₃, using

t-expansion [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]

(243−69, 243, 629)-Net over F₃ — Digital

Digital (174, 243, 629)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−69, 243, 16809)-Net in Base 3 — Upper bound on s

There is no (174, 243, 16810)-net in base 3, because

1 times m-reduction [i] would yield (174, 242, 16810)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 075718 983397 132549 955650 822724 949436 701252 316808 543256 289217 221868 044040 965713 661160 732740 798986 525424 462151 640325 > 3²⁴² [i]