MinT - Best Known (13, 13+38, s)-Nets in Base 4

Best Known (13, 13+38, s)-Nets in Base 4

(13, 13+38, 30)-Net over F₄ — Constructive and digital

Digital (13, 51, 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+38, 33)-Net over F₄ — Digital

Digital (13, 51, 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+38, 65)-Net in Base 4 — Upper bound on s

There is no (13, 51, 66)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁵¹, 66, S₄, 38), but
- the linear programming bound shows that MÂ â‰¥ 7421 079900 467185 318421 954817 545163 767808 / 1070 444375 > 4⁵¹ [i]