MinT - Best Known (169, 169+59, s)-Nets in Base 3

Best Known (169, 169+59, s)-Nets in Base 3

(169, 169+59, 288)-Net over F₃ — Constructive and digital

Digital (169, 228, 288)-net over F₃, using

9 times m-reduction [i] based on digital (169, 237, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 79, 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]

(169, 169+59, 829)-Net over F₃ — Digital

Digital (169, 228, 829)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+59, 31652)-Net in Base 3 — Upper bound on s

There is no (169, 228, 31653)-net in base 3, because

1 times m-reduction [i] would yield (169, 227, 31653)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 026250 472270 957307 537722 193293 528222 217114 092344 791092 069798 161111 928915 548752 910876 055776 332748 983579 065595 > 3²²⁷ [i]