MinT - Best Known (45, 45+69, s)-Nets in Base 16

Best Known (45, 45+69, s)-Nets in Base 16

(45, 45+69, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 114, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 114, 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]

(45, 45+69, 242)-Net over F₁₆ — Digital

Digital (45, 114, 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]

(45, 45+69, 9045)-Net in Base 16 — Upper bound on s

There is no (45, 114, 9046)-net in base 16, because

1 times m-reduction [i] would yield (45, 113, 9046)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11669 380492 085185 020454 283226 587856 856183 721290 581600 546089 176151 128096 068800 352264 686619 405604 174389 822228 021534 156029 518436 610138 432436 > 16¹¹³ [i]