MinT - Best Known (17, 17+59, s)-Nets in Base 5

Best Known (17, 17+59, s)-Nets in Base 5

(17, 17+59, 42)-Net over F₅ — Constructive and digital

Digital (17, 76, 42)-net over F₅, using

net from sequence [i] based on digital (17, 41)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]

(17, 17+59, 100)-Net in Base 5 — Upper bound on s

There is no (17, 76, 101)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁷⁶, 101, S₅, 59), but
- the linear programming bound shows that MÂ â‰¥ 333572 888464 634463 116406 006412 233142 821577 303038 793615 996837 615966 796875 / 2 053887 504779 766656 > 5⁷⁶ [i]