MinT - Best Known (196−51, 196, s)-Nets in Base 3

Best Known (196−51, 196, s)-Nets in Base 3

(196−51, 196, 288)-Net over F₃ — Constructive and digital

Digital (145, 196, 288)-net over F₃, using

5 times m-reduction [i] based on digital (145, 201, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 67, 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]

(196−51, 196, 716)-Net over F₃ — Digital

Digital (145, 196, 716)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−51, 196, 26775)-Net in Base 3 — Upper bound on s

There is no (145, 196, 26776)-net in base 3, because

1 times m-reduction [i] would yield (145, 195, 26776)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1093 132564 427631 207131 214036 039262 733672 380941 393812 164665 884234 965000 159218 128225 026436 594865 > 3¹⁹⁵ [i]