MinT - Best Known (21, 60, s)-Nets in Base 4

Best Known (21, 60, s)-Nets in Base 4

(21, 60, 34)-Net over F₄ — Constructive and digital

Digital (21, 60, 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, 60, 44)-Net over F₄ — Digital

Digital (21, 60, 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, 60, 179)-Net in Base 4 — Upper bound on s

There is no (21, 60, 180)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁰, 180, S₄, 39), but
- the linear programming bound shows that MÂ â‰¥ 64 592000 643692 089079 054839 691926 765927 402602 779909 340826 367902 235627 537241 992340 655885 516800 / 46 756581 550576 177840 289976 743881 661381 961798 582533 083517 > 4⁶⁰ [i]