MinT - Best Known (15, 15+32, s)-Nets in Base 4

Best Known (15, 15+32, s)-Nets in Base 4

(15, 15+32, 33)-Net over F₄ — Constructive and digital

Digital (15, 47, 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+32, 35)-Net over F₄ — Digital

Digital (15, 47, 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+32, 120)-Net in Base 4 — Upper bound on s

There is no (15, 47, 121)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 20631 330572 304362 432028 827629 > 4⁴⁷ [i]
extracting embedded orthogonal array [i] would yield OA(4⁴⁷, 121, S₄, 32), but
- the linear programming bound shows that MÂ â‰¥ 365 129709 190376 390301 373618 637040 010384 793045 585047 102752 276086 784000 / 18163 087858 506659 594163 938688 475283 050507 > 4⁴⁷ [i]