MinT - Best Known (80−63, 80, s)-Nets in Base 5

Best Known (80−63, 80, s)-Nets in Base 5

(80−63, 80, 42)-Net over F₅ — Constructive and digital

Digital (17, 80, 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]

(80−63, 80, 94)-Net in Base 5 — Upper bound on s

There is no (17, 80, 95)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁸⁰, 95, S₅, 63), but
- the linear programming bound shows that MÂ â‰¥ 9834 712194 160937 976153 934181 322568 974792 375229 299068 450927 734375 / 76 495968 > 5⁸⁰ [i]