MinT - Best Known (19, 19+50, s)-Nets in Base 4

Best Known (19, 19+50, s)-Nets in Base 4

(19, 19+50, 33)-Net over F₄ — Constructive and digital

Digital (19, 69, 33)-net over F₄, using

t-expansion [i] based on digital (15, 69, 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, 19+50, 41)-Net over F₄ — Digital

Digital (19, 69, 41)-net over F₄, using

t-expansion [i] based on digital (18, 69, 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, 19+50, 92)-Net in Base 4 — Upper bound on s

There is no (19, 69, 93)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁹, 93, S₄, 50), but
- the linear programming bound shows that MÂ â‰¥ 1673 524097 319220 928360 692248 874742 963116 684720 990698 078208 / 4459 155859 226025 > 4⁶⁹ [i]