MinT - Best Known (61−44, 61, s)-Nets in Base 5

Best Known (61−44, 61, s)-Nets in Base 5

(61−44, 61, 42)-Net over F₅ — Constructive and digital

Digital (17, 61, 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]

(61−44, 61, 171)-Net in Base 5 — Upper bound on s

There is no (17, 61, 172)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁶¹, 172, S₅, 44), but
- the linear programming bound shows that MÂ â‰¥ 573561 146432 903261 890838 697976 018502 051321 280095 810222 935128 477655 949281 466109 163264 253112 402002 443559 467792 510986 328125 / 128335 467227 255294 979113 150037 859458 130647 507283 557206 569267 900642 480552 611997 > 5⁶¹ [i]