MinT - Best Known (57, 57+38, s)-Nets in Base 16

Best Known (57, 57+38, s)-Nets in Base 16

(57, 57+38, 532)-Net over F₁₆ — Constructive and digital

Digital (57, 95, 532)-net over F₁₆, using

1 times m-reduction [i] based on digital (57, 96, 532)-net over F₁₆, using
- trace code for nets [i] based on digital (9, 48, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(57, 57+38, 1225)-Net over F₁₆ — Digital

Digital (57, 95, 1225)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+38, 554263)-Net in Base 16 — Upper bound on s

There is no (57, 95, 554264)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 462685 225050 092185 245698 354608 364077 224419 527942 123681 562539 169062 641032 636637 621575 826672 608204 360664 999640 993241 > 16⁹⁵ [i]