MinT - Best Known (115−50, 115, s)-Nets in Base 16

Best Known (115−50, 115, s)-Nets in Base 16

(115−50, 115, 528)-Net over F₁₆ — Constructive and digital

Digital (65, 115, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (65, 116, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 58, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(115−50, 115, 878)-Net over F₁₆ — Digital

Digital (65, 115, 878)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−50, 115, 234671)-Net in Base 16 — Upper bound on s

There is no (65, 115, 234672)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 977144 672223 934065 820611 304420 850923 942533 942719 401835 170317 647014 657823 656865 651536 284265 694328 128977 966046 256277 007683 527234 530671 145126 > 16¹¹⁵ [i]