MinT - Best Known (22, 94, s)-Nets in Base 5

Best Known (22, 94, s)-Nets in Base 5

(22, 94, 51)-Net over F₅ — Constructive and digital

Digital (22, 94, 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, 94, 128)-Net in Base 5 — Upper bound on s

There is no (22, 94, 129)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹⁴, 129, S₅, 72), but
- the linear programming bound shows that MÂ â‰¥ 2 754381 319426 228408 193865 444091 571297 567467 395753 576715 235200 200737 608611 234463 751316 070556 640625 / 4 350807 194334 256358 976373 858769 > 5⁹⁴ [i]