MinT - Best Known (79−56, 79, s)-Nets in Base 4

Best Known (79−56, 79, s)-Nets in Base 4

(79−56, 79, 34)-Net over F₄ — Constructive and digital

Digital (23, 79, 34)-net over F₄, using

t-expansion [i] based on digital (21, 79, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(79−56, 79, 45)-Net over F₄ — Digital

Digital (23, 79, 45)-net over F₄, using

net from sequence [i] based on digital (23, 44)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 23 and N(F) ≥ 45, using
  - a curve from the manYPoints database [i]

(79−56, 79, 119)-Net in Base 4 — Upper bound on s

There is no (23, 79, 120)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁷⁹, 120, S₄, 56), but
- the linear programming bound shows that MÂ â‰¥ 5497 702162 977970 118015 807544 103800 603244 229205 950971 423564 769215 948368 163519 579077 738496 / 14482 724292 377992 392159 177164 961903 510735 > 4⁷⁹ [i]