MinT - Best Known (159−137, 159, s)-Nets in Base 3

Best Known (159−137, 159, s)-Nets in Base 3

(159−137, 159, 32)-Net over F₃ — Constructive and digital

Digital (22, 159, 32)-net over F₃, using

t-expansion [i] based on digital (21, 159, 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]

(159−137, 159, 58)-Net in Base 3 — Upper bound on s

There is no (22, 159, 59)-net in base 3, because

45 times m-reduction [i] would yield (22, 114, 59)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹¹⁴, 59, S₃, 2, 92), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 81 346145 263616 227631 872337 961340 145831 465974 909120 831977 / 31 > 3¹¹⁴ [i]