MinT - Best Known (13, 13+34, s)-Nets in Base 4

Best Known (13, 13+34, s)-Nets in Base 4

(13, 13+34, 30)-Net over F₄ — Constructive and digital

Digital (13, 47, 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+34, 33)-Net over F₄ — Digital

Digital (13, 47, 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+34, 82)-Net in Base 4 — Upper bound on s

There is no (13, 47, 83)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁷, 83, S₄, 34), but
- the linear programming bound shows that MÂ â‰¥ 52 720571 155598 864034 786269 073952 563615 274024 793807 425195 470485 757374 758912 / 2526 264626 215124 582307 285701 642932 544212 018125 > 4⁴⁷ [i]