MinT - Best Known (22, 22+70, s)-Nets in Base 5

Best Known (22, 22+70, s)-Nets in Base 5

(22, 22+70, 51)-Net over F₅ — Constructive and digital

Digital (22, 92, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(22, 22+70, 136)-Net in Base 5 — Upper bound on s

There is no (22, 92, 137)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹², 137, S₅, 70), but
- the linear programming bound shows that MÂ â‰¥ 1 272921 368004 356155 684888 398710 232545 527539 532532 139387 550863 838694 581318 800968 898485 859170 932599 226944 148540 496826 171875 / 58 583462 568754 021890 472578 395903 968870 113992 078881 579392 > 5⁹² [i]