MinT - Best Known (131−67, 131, s)-Nets in Base 3

Best Known (131−67, 131, s)-Nets in Base 3

(131−67, 131, 56)-Net over F₃ — Constructive and digital

Digital (64, 131, 56)-net over F₃, using

1 times m-reduction [i] based on digital (64, 132, 56)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 49, 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, 83, 28)-net over F₃, using
    - net from sequence [i] based on digital (15, 27)-sequence over F₃ (see above)

(131−67, 131, 66)-Net over F₃ — Digital

Digital (64, 131, 66)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−67, 131, 467)-Net in Base 3 — Upper bound on s

There is no (64, 131, 468)-net in base 3, because

1 times m-reduction [i] would yield (64, 130, 468)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 112 514527 056426 634729 856265 079179 737015 108758 245730 270714 137001 > 3¹³⁰ [i]