MinT - Best Known (17, 17+62, s)-Nets in Base 5

Best Known (17, 17+62, s)-Nets in Base 5

(17, 17+62, 42)-Net over F₅ — Constructive and digital

Digital (17, 79, 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+62, 95)-Net in Base 5 — Upper bound on s

There is no (17, 79, 96)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁷⁹, 96, S₅, 62), but
- the linear programming bound shows that MÂ â‰¥ 54681 565591 073801 418345 486091 698859 354437 445290 386676 788330 078125 / 2638 671021 > 5⁷⁹ [i]