MinT - Best Known (70, 70+57, s)-Nets in Base 16

Best Known (70, 70+57, s)-Nets in Base 16

(70, 70+57, 526)-Net over F₁₆ — Constructive and digital

Digital (70, 127, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (70, 128, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 64, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(70, 70+57, 789)-Net over F₁₆ — Digital

Digital (70, 127, 789)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+57, 197433)-Net in Base 16 — Upper bound on s

There is no (70, 127, 197434)-net in base 16, because

1 times m-reduction [i] would yield (70, 126, 197434)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 52 381179 551263 574338 762916 036718 193890 965470 765036 259183 194589 350067 543519 900341 531896 735360 859314 076255 089216 826148 012777 306348 511591 292780 256873 117656 > 16¹²⁶ [i]