MinT - Best Known (34, 34+35, s)-Nets in Base 16

Best Known (34, 34+35, s)-Nets in Base 16

(34, 34+35, 257)-Net over F₁₆ — Constructive and digital

Digital (34, 69, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(34,256) in PG(68,16)) for nets [i] based on digital (0, 35, 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]

(34, 34+35, 31347)-Net in Base 16 — Upper bound on s

There is no (34, 69, 31348)-net in base 16, because

1 times m-reduction [i] would yield (34, 68, 31348)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 7589 282538 252664 877685 160830 346373 909781 544809 670904 864708 667679 072481 067368 965591 > 16⁶⁸ [i]