MinT - Best Known (60−39, 60, s)-Nets in Base 3

Best Known (60−39, 60, s)-Nets in Base 3

(60−39, 60, 32)-Net over F₃ — Constructive and digital

Digital (21, 60, 32)-net over F₃, using

net from sequence [i] based on digital (21, 31)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(60−39, 60, 79)-Net in Base 3 — Upper bound on s

There is no (21, 60, 80)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁰, 80, S₃, 39), but
- the linear programming bound shows that MÂ â‰¥ 10299 241947 274765 323111 769912 609288 895091 / 233101 383112 > 3⁶⁰ [i]