MinT - Best Known (185−85, 185, s)-Nets in Base 3

Best Known (185−85, 185, s)-Nets in Base 3

(185−85, 185, 74)-Net over F₃ — Constructive and digital

Digital (100, 185, 74)-net over F₃, using

7 times m-reduction [i] based on digital (100, 192, 74)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 73, 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, 119, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(185−85, 185, 119)-Net over F₃ — Digital

Digital (100, 185, 119)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−85, 185, 975)-Net in Base 3 — Upper bound on s

There is no (100, 185, 976)-net in base 3, because

1 times m-reduction [i] would yield (100, 184, 976)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6304 202681 460173 901627 284205 704474 954068 716640 662807 975380 622654 723593 475880 404149 031393 > 3¹⁸⁴ [i]