MinT - Best Known (180−159, 180, s)-Nets in Base 3

Best Known (180−159, 180, s)-Nets in Base 3

(180−159, 180, 32)-Net over F₃ — Constructive and digital

Digital (21, 180, 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]

(180−159, 180, 53)-Net in Base 3 — Upper bound on s

There is no (21, 180, 54)-net in base 3, because

24 times m-reduction [i] would yield (21, 156, 54)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁵⁶, 54, S₃, 3, 135), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 10159 513810 579551 549539 358785 341138 152716 364863 601403 137991 148585 180705 169291 / 34 > 3¹⁵⁶ [i]