MinT - Best Known (105, 105+101, s)-Nets in Base 3

Best Known (105, 105+101, s)-Nets in Base 3

(105, 105+101, 74)-Net over F₃ — Constructive and digital

Digital (105, 206, 74)-net over F₃, using

1 times m-reduction [i] based on digital (105, 207, 74)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 78, 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, 129, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(105, 105+101, 108)-Net over F₃ — Digital

Digital (105, 206, 108)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+101, 832)-Net in Base 3 — Upper bound on s

There is no (105, 206, 833)-net in base 3, because

1 times m-reduction [i] would yield (105, 205, 833)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 67 060870 790173 917230 300745 609740 343475 276940 863450 494034 988702 818215 002802 867436 102573 444834 540617 > 3²⁰⁵ [i]