MinT - Best Known (21−18, 21, s)-Nets in Base 5

Best Known (21−18, 21, s)-Nets in Base 5

(21−18, 21, 16)-Net over F₅ — Constructive and digital

Digital (3, 21, 16)-net over F₅, using

net from sequence [i] based on digital (3, 15)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
  - an explicitly constructive algebraic function field [i]

(21−18, 21, 22)-Net in Base 5 — Upper bound on s

There is no (3, 21, 23)-net in base 5, because

extracting embedded OOA [i] would yield OOA(5²¹, 23, S₅, 2, 18), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 92983 245849 609375 / 137 > 5²¹ [i]