MinT - Best Known (68, 68+57, s)-Nets in Base 16

Best Known (68, 68+57, s)-Nets in Base 16

(68, 68+57, 524)-Net over F₁₆ — Constructive and digital

Digital (68, 125, 524)-net over F₁₆, using

1 times m-reduction [i] based on digital (68, 126, 524)-net over F₁₆, using
- trace code for nets [i] based on digital (5, 63, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(68, 68+57, 712)-Net over F₁₆ — Digital

Digital (68, 125, 712)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+57, 161958)-Net in Base 16 — Upper bound on s

There is no (68, 125, 161959)-net in base 16, because

1 times m-reduction [i] would yield (68, 124, 161959)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 204602 312261 436829 205030 221562 629956 965619 152119 646855 576637 927652 577517 939668 855655 202620 028753 419489 089135 833046 843856 217517 130248 367433 426736 158156 > 16¹²⁴ [i]