MinT - Best Known (95−40, 95, s)-Nets in Base 16

Best Known (95−40, 95, s)-Nets in Base 16

(95−40, 95, 528)-Net over F₁₆ — Constructive and digital

Digital (55, 95, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (55, 96, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 48, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(95−40, 95, 899)-Net over F₁₆ — Digital

Digital (55, 95, 899)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−40, 95, 290247)-Net in Base 16 — Upper bound on s

There is no (55, 95, 290248)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 462688 416477 851315 740687 076484 497228 988256 556471 435982 276391 938788 550657 867958 963299 291865 678524 733782 246709 445276 > 16⁹⁵ [i]