MinT - Best Known (59−30, 59, s)-Nets in Base 16

Best Known (59−30, 59, s)-Nets in Base 16

(59−30, 59, 257)-Net over F₁₆ — Constructive and digital

Digital (29, 59, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(29,256) in PG(58,16)) for nets [i] based on digital (0, 30, 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]

(59−30, 59, 23320)-Net in Base 16 — Upper bound on s

There is no (29, 59, 23321)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 110486 933553 010146 159189 338617 189090 052251 676064 159338 150953 349965 608976 > 16⁵⁹ [i]