MinT - Best Known (118−73, 118, s)-Nets in Base 16

Best Known (118−73, 118, s)-Nets in Base 16

(118−73, 118, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 118, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 118, 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]

(118−73, 118, 242)-Net over F₁₆ — Digital

Digital (45, 118, 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]

(118−73, 118, 7779)-Net in Base 16 — Upper bound on s

There is no (45, 118, 7780)-net in base 16, because

1 times m-reduction [i] would yield (45, 117, 7780)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 765 473337 540100 581394 121955 228564 845337 088955 427686 473626 710779 819378 584111 153107 575923 260649 910552 226778 622844 132190 076777 016424 963319 030576 > 16¹¹⁷ [i]