MinT - Best Known (55−28, 55, s)-Nets in Base 16

Best Known (55−28, 55, s)-Nets in Base 16

(55−28, 55, 257)-Net over F₁₆ — Constructive and digital

Digital (27, 55, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(27,256) in PG(54,16)) for nets [i] based on digital (0, 28, 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]

(55−28, 55, 21661)-Net in Base 16 — Upper bound on s

There is no (27, 55, 21662)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 685523 639923 318803 149307 206877 338620 121652 479371 851679 036339 410696 > 16⁵⁵ [i]