MinT - Best Known (69, 161, s)-Nets in Base 3

Best Known (69, 161, s)-Nets in Base 3

(69, 161, 48)-Net over F₃ — Constructive and digital

Digital (69, 161, 48)-net over F₃, using

t-expansion [i] based on digital (45, 161, 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]

(69, 161, 82)-Net over F₃ — Digital

Digital (69, 161, 82)-net over F₃, using

net from sequence [i] based on digital (69, 81)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 69 and N(F) ≥ 82, using
  - Drinfeld modules of rank 1 [i]

(69, 161, 377)-Net in Base 3 — Upper bound on s

There is no (69, 161, 378)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 70893 553977 116383 174168 950941 184837 425967 605586 298110 005685 939603 416733 242141 > 3¹⁶¹ [i]