MinT - Best Known (49−36, 49, s)-Nets in Base 4

Best Known (49−36, 49, s)-Nets in Base 4

(49−36, 49, 30)-Net over F₄ — Constructive and digital

Digital (13, 49, 30)-net over F₄, using

net from sequence [i] based on digital (13, 29)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
  - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(49−36, 49, 33)-Net over F₄ — Digital

Digital (13, 49, 33)-net over F₄, using

net from sequence [i] based on digital (13, 32)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 33, using
  - Drinfeld modules of rank 1 [i]

(49−36, 49, 71)-Net in Base 4 — Upper bound on s

There is no (13, 49, 72)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁹, 72, S₄, 36), but
- the linear programming bound shows that MÂ â‰¥ 383712 868481 228941 339475 346716 547702 487685 005312 / 1 144084 399499 160119 > 4⁴⁹ [i]