MinT - Best Known (40−36, 40, s)-Nets in Base 5

Best Known (40−36, 40, s)-Nets in Base 5

(40−36, 40, 18)-Net over F₅ — Constructive and digital

Digital (4, 40, 18)-net over F₅, using

net from sequence [i] based on digital (4, 17)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 4 and N(F) ≥ 18, using
  - an explicitly constructive algebraic function field [i]

(40−36, 40, 24)-Net in Base 5 — Upper bound on s

There is no (4, 40, 25)-net in base 5, because

11 times m-reduction [i] would yield (4, 29, 25)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5²⁹, 25, S₅, 2, 25), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 120468 437671 661376 953125 / 639 > 5²⁹ [i]