MinT - Best Known (23, 23+24, s)-Nets in Base 16

Best Known (23, 23+24, s)-Nets in Base 16

(23, 23+24, 257)-Net over F₁₆ — Constructive and digital

Digital (23, 47, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(23,256) in PG(46,16)) for nets [i] based on digital (0, 24, 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]

(23, 23+24, 18334)-Net in Base 16 — Upper bound on s

There is no (23, 47, 18335)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 392 572029 612566 465433 453402 262943 091290 107231 008251 095801 > 16⁴⁷ [i]