MinT - Best Known (20, 20+49, s)-Nets in Base 4

Best Known (20, 20+49, s)-Nets in Base 4

(20, 20+49, 33)-Net over F₄ — Constructive and digital

Digital (20, 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]

(20, 20+49, 41)-Net over F₄ — Digital

Digital (20, 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]

(20, 20+49, 111)-Net in Base 4 — Upper bound on s

There is no (20, 69, 112)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁹, 112, S₄, 49), but
- the linear programming bound shows that MÂ â‰¥ 2547 375594 089649 466260 876048 964586 975313 051261 505507 833758 636632 680851 295239 667712 / 7046 554421 803103 481350 606505 887965 178125 > 4⁶⁹ [i]