MinT - Best Known (50−39, 50, s)-Nets in Base 5

Best Known (50−39, 50, s)-Nets in Base 5

(50−39, 50, 32)-Net over F₅ — Constructive and digital

Digital (11, 50, 32)-net over F₅, using

net from sequence [i] based on digital (11, 31)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(50−39, 50, 85)-Net in Base 5 — Upper bound on s

There is no (11, 50, 86)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵⁰, 86, S₅, 39), but
- the linear programming bound shows that MÂ â‰¥ 6 266234 124941 870690 134946 783936 446664 428528 529700 024307 658168 254420 161247 253417 968750 / 66 533121 872640 841604 791025 731269 659825 374684 195761 > 5⁵⁰ [i]