MinT - Best Known (201−65, 201, s)-Nets in Base 3

Best Known (201−65, 201, s)-Nets in Base 3

(201−65, 201, 162)-Net over F₃ — Constructive and digital

Digital (136, 201, 162)-net over F₃, using

7 times m-reduction [i] based on digital (136, 208, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 104, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(201−65, 201, 352)-Net over F₃ — Digital

Digital (136, 201, 352)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(201−65, 201, 6104)-Net in Base 3 — Upper bound on s

There is no (136, 201, 6105)-net in base 3, because

1 times m-reduction [i] would yield (136, 200, 6105)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 266746 770776 142755 383254 302448 530558 069109 904324 926476 410677 970714 736475 854120 531680 244252 327553 > 3²⁰⁰ [i]