MinT - Best Known (31−28, 31, s)-Nets in Base 16

Best Known (31−28, 31, s)-Nets in Base 16

(31−28, 31, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 31, 38)-net over F₁₆, using

net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
  - a function field by SÃ©mirat [i]

(31−28, 31, 167)-Net in Base 16 — Upper bound on s

There is no (3, 31, 168)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16³¹, 168, S₁₆, 28), but
- the linear programming bound shows that MÂ â‰¥ 1 495536 208320 731259 156955 842664 614776 585079 121203 389295 230976 / 68613 124069 046094 679541 > 16³¹ [i]