MinT - Best Known (21, 21+41, s)-Nets in Base 4

Best Known (21, 21+41, s)-Nets in Base 4

(21, 21+41, 34)-Net over F₄ — Constructive and digital

Digital (21, 62, 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+41, 44)-Net over F₄ — Digital

Digital (21, 62, 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+41, 168)-Net in Base 4 — Upper bound on s

There is no (21, 62, 169)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶², 169, S₄, 41), but
- the linear programming bound shows that MÂ â‰¥ 25171 060604 496198 113359 740373 368869 999898 334565 616347 337981 288178 184867 760688 088668 492201 991549 747200 / 1168 180553 676758 470189 656469 231757 605150 850528 809269 341506 088169 > 4⁶² [i]