MinT - Best Known (125−108, 125, s)-Nets in Base 5

Best Known (125−108, 125, s)-Nets in Base 5

(125−108, 125, 42)-Net over F₅ — Constructive and digital

Digital (17, 125, 42)-net over F₅, using

net from sequence [i] based on digital (17, 41)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]

(125−108, 125, 92)-Net in Base 5 — Upper bound on s

There is no (17, 125, 93)-net in base 5, because

44 times m-reduction [i] would yield (17, 81, 93)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5⁸¹, 93, S₅, 64), but
  - the linear programming bound shows that MÂ â‰¥ 615521 895906 900376 246461 033258 317030 458783 847279 846668 243408 203125 / 1347 475701 > 5⁸¹ [i]