MinT - Best Known (42−31, 42, s)-Nets in Base 5

Best Known (42−31, 42, s)-Nets in Base 5

(42−31, 42, 32)-Net over F₅ — Constructive and digital

Digital (11, 42, 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]

(42−31, 42, 119)-Net in Base 5 — Upper bound on s

There is no (11, 42, 120)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴², 120, S₅, 31), but
- the linear programming bound shows that MÂ â‰¥ 662672 307412 129870 469164 413977 180562 845393 992366 734892 129898 071289 062500 / 2 653474 185364 441465 462240 730332 148784 303407 > 5⁴² [i]