MinT - Best Known (21, 21+22, s)-Nets in Base 16

Best Known (21, 21+22, s)-Nets in Base 16

(21, 21+22, 257)-Net over F₁₆ — Constructive and digital

Digital (21, 43, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(21,256) in PG(42,16)) for nets [i] based on digital (0, 22, 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]

(21, 21+22, 16664)-Net in Base 16 — Upper bound on s

There is no (21, 43, 16665)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 5988 936776 644431 145692 331892 378435 423992 540349 940976 > 16⁴³ [i]