MinT - Best Known (49−25, 49, s)-Nets in Base 16

Best Known (49−25, 49, s)-Nets in Base 16

(49−25, 49, 257)-Net over F₁₆ — Constructive and digital

Digital (24, 49, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(24,256) in PG(48,16)) for nets [i] based on digital (0, 25, 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]

(49−25, 49, 23101)-Net in Base 16 — Upper bound on s

There is no (24, 49, 23102)-net in base 16, because

1 times m-reduction [i] would yield (24, 48, 23102)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6280 207677 256815 715054 216728 409532 504231 289781 588563 685411 > 16⁴⁸ [i]