MinT - Best Known (196−93, 196, s)-Nets in Base 3

Best Known (196−93, 196, s)-Nets in Base 3

(196−93, 196, 74)-Net over F₃ — Constructive and digital

Digital (103, 196, 74)-net over F₃, using

5 times m-reduction [i] based on digital (103, 201, 74)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 76, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
  2. digital (27, 125, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(196−93, 196, 114)-Net over F₃ — Digital

Digital (103, 196, 114)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−93, 196, 903)-Net in Base 3 — Upper bound on s

There is no (103, 196, 904)-net in base 3, because

1 times m-reduction [i] would yield (103, 195, 904)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1129 553247 463499 369245 121894 762304 902422 890857 115098 381315 532821 632131 003381 849956 527542 790065 > 3¹⁹⁵ [i]