MinT - Best Known (46, 46+69, s)-Nets in Base 16

Best Known (46, 46+69, s)-Nets in Base 16

(46, 46+69, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 115, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 115, 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]

(46, 46+69, 243)-Net over F₁₆ — Digital

Digital (46, 115, 243)-net over F₁₆, using

net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
  - a curve from the manYPoints database [i]

(46, 46+69, 9815)-Net in Base 16 — Upper bound on s

There is no (46, 115, 9816)-net in base 16, because

1 times m-reduction [i] would yield (46, 114, 9816)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 186596 216733 201247 721299 660525 062024 079510 720576 338491 000147 881537 511036 590296 239811 091243 600868 550881 516065 865834 243523 688315 500220 829386 > 16¹¹⁴ [i]