MinT - Best Known (122−61, 122, s)-Nets in Base 3

Best Known (122−61, 122, s)-Nets in Base 3

(122−61, 122, 56)-Net over F₃ — Constructive and digital

Digital (61, 122, 56)-net over F₃, using

1 times m-reduction [i] based on digital (61, 123, 56)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 46, 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, 77, 28)-net over F₃, using
    - net from sequence [i] based on digital (15, 27)-sequence over F₃ (see above)

(122−61, 122, 66)-Net over F₃ — Digital

Digital (61, 122, 66)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−61, 122, 477)-Net in Base 3 — Upper bound on s

There is no (61, 122, 478)-net in base 3, because

1 times m-reduction [i] would yield (61, 121, 478)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5655 376886 548689 653420 974923 337779 046200 584512 278118 138773 > 3¹²¹ [i]