MinT - Best Known (14, 14+38, s)-Nets in Base 4

Best Known (14, 14+38, s)-Nets in Base 4

(14, 14+38, 30)-Net over F₄ — Constructive and digital

Digital (14, 52, 30)-net over F₄, using

t-expansion [i] based on digital (13, 52, 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]

(14, 14+38, 33)-Net over F₄ — Digital

Digital (14, 52, 33)-net over F₄, using

t-expansion [i] based on digital (13, 52, 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]

(14, 14+38, 76)-Net in Base 4 — Upper bound on s

There is no (14, 52, 77)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁵², 77, S₄, 38), but
- the linear programming bound shows that MÂ â‰¥ 178964 168015 271617 653478 330356 832179 607270 588416 / 8492 957066 104875 > 4⁵² [i]