MinT - Best Known (23−20, 23, s)-Nets in Base 5

Best Known (23−20, 23, s)-Nets in Base 5

(23−20, 23, 16)-Net over F₅ — Constructive and digital

Digital (3, 23, 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]

(23−20, 23, 20)-Net in Base 5 — Upper bound on s

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

extracting embedded OOA [i] would yield OOA(5²³, 21, S₅, 2, 20), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 12 767314 910888 671875 / 1049 > 5²³ [i]