MinT - Best Known (68, 68+55, s)-Nets in Base 16

Best Known (68, 68+55, s)-Nets in Base 16

(68, 68+55, 526)-Net over F₁₆ — Constructive and digital

Digital (68, 123, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (68, 124, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 62, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(68, 68+55, 786)-Net over F₁₆ — Digital

Digital (68, 123, 786)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+55, 200965)-Net in Base 16 — Upper bound on s

There is no (68, 123, 200966)-net in base 16, because

1 times m-reduction [i] would yield (68, 122, 200966)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 799 198377 436852 474024 436470 823140 984452 709618 350124 361450 104825 212750 052951 133241 631824 317792 827642 060795 364854 717689 008243 509072 751844 178718 827456 > 16¹²² [i]