MinT - Best Known (17, 17+56, s)-Nets in Base 5

Best Known (17, 17+56, s)-Nets in Base 5

(17, 17+56, 42)-Net over F₅ — Constructive and digital

Digital (17, 73, 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]

(17, 17+56, 112)-Net in Base 5 — Upper bound on s

There is no (17, 73, 113)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁷³, 113, S₅, 56), but
- the linear programming bound shows that MÂ â‰¥ 337811 585954 403046 973013 511278 094593 172405 927467 629325 054352 361357 157263 910266 919992 864131 927490 234375 / 295 619144 563353 071093 742262 323377 673476 554685 952918 > 5⁷³ [i]