MinT - Best Known (163, 163+65, s)-Nets in Base 3

Best Known (163, 163+65, s)-Nets in Base 3

(163, 163+65, 288)-Net over F₃ — Constructive and digital

Digital (163, 228, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 76, 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]

(163, 163+65, 587)-Net over F₃ — Digital

Digital (163, 228, 587)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+65, 15472)-Net in Base 3 — Upper bound on s

There is no (163, 228, 15473)-net in base 3, because

1 times m-reduction [i] would yield (163, 227, 15473)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 029610 323140 017444 897337 645782 298155 805721 313632 130516 904851 503184 693276 208884 955754 619071 051823 031612 716673 > 3²²⁷ [i]