MinT - Best Known (9, 9+33, s)-Nets in Base 5

Best Known (9, 9+33, s)-Nets in Base 5

(9, 9+33, 26)-Net over F₅ — Constructive and digital

Digital (9, 42, 26)-net over F₅, using

net from sequence [i] based on digital (9, 25)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
  - an explicitly constructive algebraic function field [i]

(9, 9+33, 74)-Net in Base 5 — Upper bound on s

There is no (9, 42, 75)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴², 75, S₅, 33), but
- the linear programming bound shows that MÂ â‰¥ 11 286125 110685 811566 010497 641086 066464 923086 926177 120403 735898 435115 814208 984375 / 48 151576 520629 405287 947768 575959 673496 311856 302903 > 5⁴² [i]