MinT - Best Known (68, 68+54, s)-Nets in Base 16

Best Known (68, 68+54, s)-Nets in Base 16

(68, 68+54, 528)-Net over F₁₆ — Constructive and digital

Digital (68, 122, 528)-net over F₁₆, using

trace code for nets [i] based on digital (7, 61, 264)-net over F₂₅₆, using
- net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(68, 68+54, 829)-Net over F₁₆ — Digital

Digital (68, 122, 829)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+54, 200965)-Net in Base 16 — Upper bound on s

There is no (68, 122, 200966)-net in base 16, because

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]