MinT - Best Known (49−38, 49, s)-Nets in Base 5

Best Known (49−38, 49, s)-Nets in Base 5

(49−38, 49, 32)-Net over F₅ — Constructive and digital

Digital (11, 49, 32)-net over F₅, using

net from sequence [i] based on digital (11, 31)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(49−38, 49, 90)-Net in Base 5 — Upper bound on s

There is no (11, 49, 91)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁹, 91, S₅, 38), but
- the linear programming bound shows that MÂ â‰¥ 1086 257987 241163 736022 714215 674574 549744 357411 501413 445595 034129 868490 748454 248456 284034 170364 893867 599676 013924 181461 334228 515625 / 58336 817128 622807 772567 762900 281184 931180 836623 253840 902030 575546 253757 728488 400715 971702 082144 > 5⁴⁹ [i]