MinT - Best Known (201−99, 201, s)-Nets in Base 3

Best Known (201−99, 201, s)-Nets in Base 3

(201−99, 201, 73)-Net over F₃ — Constructive and digital

Digital (102, 201, 73)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 75, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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, 126, 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]

(201−99, 201, 105)-Net over F₃ — Digital

Digital (102, 201, 105)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(201−99, 201, 799)-Net in Base 3 — Upper bound on s

There is no (102, 201, 800)-net in base 3, because

1 times m-reduction [i] would yield (102, 200, 800)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 276780 896583 473961 161070 814329 746892 678604 525643 577121 449579 900572 535548 194960 831711 457145 694785 > 3²⁰⁰ [i]