MinT - Best Known (91−69, 91, s)-Nets in Base 5

Best Known (91−69, 91, s)-Nets in Base 5

(91−69, 91, 51)-Net over F₅ — Constructive and digital

Digital (22, 91, 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]

(91−69, 91, 142)-Net in Base 5 — Upper bound on s

There is no (22, 91, 143)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹¹, 143, S₅, 69), but
- the linear programming bound shows that MÂ â‰¥ 10818 633622 696411 375392 776604 547420 521081 254765 585985 900970 666207 559389 662199 115127 169733 556466 990620 492651 942186 057567 596435 546875 / 2 557518 484922 431555 758338 082503 434887 900718 755784 631565 540511 421691 > 5⁹¹ [i]