MinT - Best Known (19, 60, s)-Nets in Base 4

Best Known (19, 60, s)-Nets in Base 4

(19, 60, 33)-Net over F₄ — Constructive and digital

Digital (19, 60, 33)-net over F₄, using

t-expansion [i] based on digital (15, 60, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(19, 60, 41)-Net over F₄ — Digital

Digital (19, 60, 41)-net over F₄, using

t-expansion [i] based on digital (18, 60, 41)-net over F₄, using
- net from sequence [i] based on digital (18, 40)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 18 and N(F) ≥ 41, using
    - Drinfeld modules of rank 1 [i]

(19, 60, 139)-Net in Base 4 — Upper bound on s

There is no (19, 60, 140)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁰, 140, S₄, 41), but
- the linear programming bound shows that MÂ â‰¥ 879403 484026 313933 129107 893130 654952 488416 854359 107391 996054 021035 128392 974988 409099 175067 144881 999812 150052 449544 895148 851200 / 619301 085252 374849 001693 023953 651889 253595 081048 920563 530321 558861 109148 317743 673454 318139 > 4⁶⁰ [i]