MinT - Best Known (205−95, 205, s)-Nets in Base 3

Best Known (205−95, 205, s)-Nets in Base 3

(205−95, 205, 76)-Net over F₃ — Constructive and digital

Digital (110, 205, 76)-net over F₃, using

5 times m-reduction [i] based on digital (110, 210, 76)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 65, 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, 145, 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]

(205−95, 205, 127)-Net over F₃ — Digital

Digital (110, 205, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−95, 205, 1035)-Net in Base 3 — Upper bound on s

There is no (110, 205, 1036)-net in base 3, because

1 times m-reduction [i] would yield (110, 204, 1036)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 801536 553429 982112 449041 897970 772193 661548 683832 238435 052367 419102 391612 269255 099424 316897 030545 > 3²⁰⁴ [i]