MinT - Best Known (108−63, 108, s)-Nets in Base 16

Best Known (108−63, 108, s)-Nets in Base 16

(108−63, 108, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 108, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 108, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(108−63, 108, 242)-Net over F₁₆ — Digital

Digital (45, 108, 242)-net over F₁₆, using

net from sequence [i] based on digital (45, 241)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 45 and N(F) ≥ 242, using
  - a curve from the manYPoints database [i]

(108−63, 108, 11843)-Net in Base 16 — Upper bound on s

There is no (45, 108, 11844)-net in base 16, because

1 times m-reduction [i] would yield (45, 107, 11844)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 694 442716 364480 241087 405800 962260 528580 659499 246749 580160 547231 828766 857467 576499 322207 409064 079723 555801 574882 467226 699106 064336 > 16¹⁰⁷ [i]