MinT - Best Known (20, 20+54, s)-Nets in Base 4

Best Known (20, 20+54, s)-Nets in Base 4

(20, 20+54, 33)-Net over F₄ — Constructive and digital

Digital (20, 74, 33)-net over F₄, using

t-expansion [i] based on digital (15, 74, 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]

(20, 20+54, 41)-Net over F₄ — Digital

Digital (20, 74, 41)-net over F₄, using

t-expansion [i] based on digital (18, 74, 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]

(20, 20+54, 92)-Net in Base 4 — Upper bound on s

There is no (20, 74, 93)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁷⁴, 93, S₄, 54), but
- the linear programming bound shows that MÂ â‰¥ 192 364622 691484 436471 917533 362873 754047 265742 920473 378816 / 445079 156093 > 4⁷⁴ [i]