MinT - Best Known (106, 199, s)-Nets in Base 3

Best Known (106, 199, s)-Nets in Base 3

(106, 199, 76)-Net over F₃ — Constructive and digital

Digital (106, 199, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 61, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
2. digital (45, 138, 48)-net over F₃, using
  - net from sequence [i] based on digital (45, 47)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
      - an explicitly constructive algebraic function field [i]

(106, 199, 121)-Net over F₃ — Digital

Digital (106, 199, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 199, 973)-Net in Base 3 — Upper bound on s

There is no (106, 199, 974)-net in base 3, because

1 times m-reduction [i] would yield (106, 198, 974)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29950 265071 552422 110497 447598 765698 565603 431282 555073 743889 681347 994925 435361 708915 268676 336981 > 3¹⁹⁸ [i]