MinT - Best Known (15, 15+18, s)-Nets in Base 4

Best Known (15, 15+18, s)-Nets in Base 4

(15, 15+18, 33)-Net over F₄ — Constructive and digital

Digital (15, 33, 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, 15+18, 35)-Net over F₄ — Digital

Digital (15, 33, 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, 15+18, 216)-Net in Base 4 — Upper bound on s

There is no (15, 33, 217)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 76 749341 876169 173452 > 4³³ [i]