MinT - Best Known (194−93, 194, s)-Nets in Base 3

Best Known (194−93, 194, s)-Nets in Base 3

(194−93, 194, 74)-Net over F₃ — Constructive and digital

Digital (101, 194, 74)-net over F₃, using

1 times m-reduction [i] based on digital (101, 195, 74)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 74, 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, 121, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(194−93, 194, 110)-Net over F₃ — Digital

Digital (101, 194, 110)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−93, 194, 859)-Net in Base 3 — Upper bound on s

There is no (101, 194, 860)-net in base 3, because

1 times m-reduction [i] would yield (101, 193, 860)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 126 815249 032369 879278 631798 585378 436953 621390 986163 695173 220184 381194 725925 227017 904750 993257 > 3¹⁹³ [i]