MinT - Best Known (22, 22+78, s)-Nets in Base 5

Best Known (22, 22+78, s)-Nets in Base 5

(22, 22+78, 51)-Net over F₅ — Constructive and digital

Digital (22, 100, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(22, 22+78, 116)-Net in Base 5 — Upper bound on s

There is no (22, 100, 117)-net in base 5, because

1 times m-reduction [i] would yield (22, 99, 117)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5⁹⁹, 117, S₅, 77), but
  - the linear programming bound shows that MÂ â‰¥ 1856 586827 495109 693107 965362 093462 886026 486169 388505 231836 461462 080478 668212 890625 / 1 144811 144204 > 5⁹⁹ [i]