MinT - Best Known (83−60, 83, s)-Nets in Base 4

Best Known (83−60, 83, s)-Nets in Base 4

(83−60, 83, 34)-Net over F₄ — Constructive and digital

Digital (23, 83, 34)-net over F₄, using

t-expansion [i] based on digital (21, 83, 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]

(83−60, 83, 45)-Net over F₄ — Digital

Digital (23, 83, 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]

(83−60, 83, 104)-Net in Base 4 — Upper bound on s

There is no (23, 83, 105)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁸³, 105, S₄, 60), but
- the linear programming bound shows that MÂ â‰¥ 171 135792 025024 709742 026030 830451 849663 731988 474278 737195 610287 374336 / 1 755195 798004 964909 > 4⁸³ [i]