MinT - Best Known (52−41, 52, s)-Nets in Base 5

Best Known (52−41, 52, s)-Nets in Base 5

(52−41, 52, 32)-Net over F₅ — Constructive and digital

Digital (11, 52, 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]

(52−41, 52, 72)-Net in Base 5 — Upper bound on s

There is no (11, 52, 73)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵², 73, S₅, 41), but
- the linear programming bound shows that MÂ â‰¥ 24983 915070 143913 883526 920471 922494 471073 150634 765625 / 10306 429071 722784 > 5⁵² [i]