MinT - Best Known (154−85, 154, s)-Nets in Base 3

Best Known (154−85, 154, s)-Nets in Base 3

(154−85, 154, 48)-Net over F₃ — Constructive and digital

Digital (69, 154, 48)-net over F₃, using

t-expansion [i] based on digital (45, 154, 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]

(154−85, 154, 82)-Net over F₃ — Digital

Digital (69, 154, 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]

(154−85, 154, 411)-Net in Base 3 — Upper bound on s

There is no (69, 154, 412)-net in base 3, because

1 times m-reduction [i] would yield (69, 153, 412)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 252697 204266 004106 047071 734390 164170 726021 301771 734017 416964 669206 033865 > 3¹⁵³ [i]