MinT - Best Known (21, 21+50, s)-Nets in Base 4

Best Known (21, 21+50, s)-Nets in Base 4

(21, 21+50, 34)-Net over F₄ — Constructive and digital

Digital (21, 71, 34)-net over F₄, using

net from sequence [i] based on digital (21, 33)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
  - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(21, 21+50, 44)-Net over F₄ — Digital

Digital (21, 71, 44)-net over F₄, using

net from sequence [i] based on digital (21, 43)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 44, using
  - a curve from the manYPoints database [i]

(21, 21+50, 122)-Net in Base 4 — Upper bound on s

There is no (21, 71, 123)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁷¹, 123, S₄, 50), but
- the linear programming bound shows that MÂ â‰¥ 9 730118 463185 507154 765323 528492 893549 916288 299079 456597 807788 957346 771116 833087 936844 982953 293596 095145 402081 214464 / 1 623445 023688 134175 655633 230735 269042 424566 381349 122269 061602 996614 225025 > 4⁷¹ [i]