MinT - Best Known (17, 17+43, s)-Nets in Base 5

Best Known (17, 17+43, s)-Nets in Base 5

(17, 17+43, 42)-Net over F₅ — Constructive and digital

Digital (17, 60, 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+43, 176)-Net in Base 5 — Upper bound on s

There is no (17, 60, 177)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁶⁰, 177, S₅, 43), but
- the linear programming bound shows that MÂ â‰¥ 44251 528081 509077 735598 452107 394672 892278 359803 017223 146162 670352 180867 894276 161678 135395 050048 828125 / 50068 492325 703590 395542 548475 114167 196751 548419 572687 939492 > 5⁶⁰ [i]