MinT - Best Known (46, 46+75, s)-Nets in Base 16

Best Known (46, 46+75, s)-Nets in Base 16

(46, 46+75, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 121, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 121, 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+75, 243)-Net over F₁₆ — Digital

Digital (46, 121, 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+75, 7833)-Net in Base 16 — Upper bound on s

There is no (46, 121, 7834)-net in base 16, because

1 times m-reduction [i] would yield (46, 120, 7834)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 132784 240009 817534 512514 147976 169878 908356 138635 375398 278323 810177 803716 369412 149000 308611 650541 129658 499677 033355 261149 133468 943476 388405 865496 > 16¹²⁰ [i]