MinT - Best Known (31, 63, s)-Nets in Base 16

Best Known (31, 63, s)-Nets in Base 16

(31, 63, 257)-Net over F₁₆ — Constructive and digital

Digital (31, 63, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(31,256) in PG(62,16)) for nets [i] based on digital (0, 32, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(31, 63, 24975)-Net in Base 16 — Upper bound on s

There is no (31, 63, 24976)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 7237 515063 440020 587122 804355 062367 973070 165212 498879 832985 891004 042933 470616 > 16⁶³ [i]