MinT - Best Known (53−48, 53, s)-Nets in Base 16

Best Known (53−48, 53, s)-Nets in Base 16

(53−48, 53, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 53, 49)-net over F₁₆, using

net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
  - a function field by SÃ©mirat [i]

(53−48, 53, 237)-Net in Base 16 — Upper bound on s

There is no (5, 53, 238)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁵³, 238, S₁₆, 48), but
- the linear programming bound shows that MÂ â‰¥ 262 605019 071495 500447 369518 214411 738986 395634 254499 333013 983712 806403 882118 265493 074476 059701 805056 / 39655 536381 979892 976662 877822 652261 > 16⁵³ [i]