MinT - Best Known (151−80, 151, s)-Nets in Base 3

Best Known (151−80, 151, s)-Nets in Base 3

(151−80, 151, 56)-Net over F₃ — Constructive and digital

Digital (71, 151, 56)-net over F₃, using

2 times m-reduction [i] based on digital (71, 153, 56)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 56, 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 (15, 97, 28)-net over F₃, using
    - net from sequence [i] based on digital (15, 27)-sequence over F₃ (see above)

(151−80, 151, 84)-Net over F₃ — Digital

Digital (71, 151, 84)-net over F₃, using

net from sequence [i] based on digital (71, 83)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(151−80, 151, 460)-Net in Base 3 — Upper bound on s

There is no (71, 151, 461)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 154192 046512 540017 614256 688375 448635 892624 295684 846714 957230 999924 148449 > 3¹⁵¹ [i]