MinT - Best Known (13, 13+33, s)-Nets in Base 4

Best Known (13, 13+33, s)-Nets in Base 4

(13, 13+33, 30)-Net over F₄ — Constructive and digital

Digital (13, 46, 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]

(13, 13+33, 33)-Net over F₄ — Digital

Digital (13, 46, 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]

(13, 13+33, 88)-Net in Base 4 — Upper bound on s

There is no (13, 46, 89)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁶, 89, S₄, 33), but
- the linear programming bound shows that MÂ â‰¥ 159948 754090 845526 538000 065296 234178 559990 299122 417191 613523 054637 510362 523087 608926 611865 440230 434765 845983 597818 865036 995130 058350 788608 / 31 655830 017094 855639 908154 532004 566126 868766 376087 543277 919844 313859 261385 645064 532693 335140 575232 262538 565325 > 4⁴⁶ [i]