MinT - Best Known (17, 17+61, s)-Nets in Base 5

Best Known (17, 17+61, s)-Nets in Base 5

(17, 17+61, 42)-Net over F₅ — Constructive and digital

Digital (17, 78, 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+61, 96)-Net in Base 5 — Upper bound on s

There is no (17, 78, 97)-net in base 5, because

1 times m-reduction [i] would yield (17, 77, 97)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5⁷⁷, 97, S₅, 60), but
  - the linear programming bound shows that MÂ â‰¥ 42984 474039 112227 940729 755982 195159 358383 307335 316203 534603 118896 484375 / 63867 353394 614679 > 5⁷⁷ [i]