MinT - Best Known (55−44, 55, s)-Nets in Base 5

Best Known (55−44, 55, s)-Nets in Base 5

(55−44, 55, 32)-Net over F₅ — Constructive and digital

Digital (11, 55, 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]

(55−44, 55, 65)-Net in Base 5 — Upper bound on s

There is no (11, 55, 66)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵⁵, 66, S₅, 44), but
- the linear programming bound shows that MÂ â‰¥ 975608 482889 356309 897266 328334 808349 609375 / 3111 > 5⁵⁵ [i]