MinT - Best Known (119−53, 119, s)-Nets in Base 16

Best Known (119−53, 119, s)-Nets in Base 16

(119−53, 119, 526)-Net over F₁₆ — Constructive and digital

Digital (66, 119, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (66, 120, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 60, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(119−53, 119, 784)-Net over F₁₆ — Digital

Digital (66, 119, 784)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−53, 119, 205127)-Net in Base 16 — Upper bound on s

There is no (66, 119, 205128)-net in base 16, because

1 times m-reduction [i] would yield (66, 118, 205128)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12195 110947 599540 521664 001696 259573 256018 721319 027022 850948 963825 706698 567518 298019 510718 885219 444462 040583 181852 989289 852646 270539 215662 454296 > 16¹¹⁸ [i]