MinT - Best Known (9, 9+∞, s)-Nets in Base 5

Best Known (9, 9+∞, s)-Nets in Base 5

(9, 9+∞, 26)-Net over F₅ — Constructive and digital

Digital (9, m, 26)-net over F₅ for arbitrarily large m, using

net from sequence [i] based on digital (9, 25)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
  - an explicitly constructive algebraic function field [i]

(9, 9+∞, 48)-Net in Base 5 — Upper bound on s

There is no (9, m, 49)-net in base 5 for arbitrarily large m, because

m-reduction [i] would yield (9, 95, 49)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5⁹⁵, 49, S₅, 2, 86), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 239 813715 187187 588845 165483 845967 013820 654756 273142 993450 164794 921875 / 87 > 5⁹⁵ [i]