MinT - Best Known (15, 53, s)-Nets in Base 4

Best Known (15, 53, s)-Nets in Base 4

(15, 53, 33)-Net over F₄ — Constructive and digital

Digital (15, 53, 33)-net over F₄, using

net from sequence [i] based on digital (15, 32)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]

(15, 53, 35)-Net over F₄ — Digital

Digital (15, 53, 35)-net over F₄, using

net from sequence [i] based on digital (15, 34)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 35, using
  - a curve from the manYPoints database [i]

(15, 53, 92)-Net in Base 4 — Upper bound on s

There is no (15, 53, 93)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁵³, 93, S₄, 38), but
- the linear programming bound shows that MÂ â‰¥ 75 732845 984145 428780 199922 279583 407868 241018 898271 306741 529817 383686 091619 434496 / 921595 659344 088994 644725 748885 291293 959320 238665 > 4⁵³ [i]