MinT - Best Known (5, 5+44, s)-Nets in Base 16

Best Known (5, 5+44, s)-Nets in Base 16

(5, 5+44, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 49, 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]

(5, 5+44, 251)-Net in Base 16 — Upper bound on s

There is no (5, 49, 252)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴⁹, 252, S₁₆, 44), but
- the linear programming bound shows that MÂ â‰¥ 723075 987677 419788 869947 707228 555123 270965 321140 158197 768094 595627 878516 444780 399288 538937 374447 501312 / 7 179888 806566 331088 677519 366744 605867 794517 > 16⁴⁹ [i]