MinT - Best Known (195−94, 195, s)-Nets in Base 3

Best Known (195−94, 195, s)-Nets in Base 3

(195−94, 195, 74)-Net over F₃ — Constructive and digital

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)

(195−94, 195, 108)-Net over F₃ — Digital

Digital (101, 195, 108)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−94, 195, 830)-Net in Base 3 — Upper bound on s

There is no (101, 195, 831)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1109 394053 073806 259726 256981 554207 336158 768160 231297 752644 285437 709895 927699 432215 541629 574307 > 3¹⁹⁵ [i]