MinT - Best Known (11, 11+48, s)-Nets in Base 5

Best Known (11, 11+48, s)-Nets in Base 5

(11, 11+48, 32)-Net over F₅ — Constructive and digital

Digital (11, 59, 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]

(11, 11+48, 64)-Net in Base 5 — Upper bound on s

There is no (11, 59, 65)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵⁹, 65, S₅, 48), but
- the linear programming bound shows that MÂ â‰¥ 802 309607 639273 281165 515072 643756 866455 078125 / 3773 > 5⁵⁹ [i]