MinT - Best Known (52, 52+37, s)-Nets in Base 16

Best Known (52, 52+37, s)-Nets in Base 16

(52, 52+37, 528)-Net over F₁₆ — Constructive and digital

Digital (52, 89, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (52, 90, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 45, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(52, 52+37, 921)-Net over F₁₆ — Digital

Digital (52, 89, 921)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+37, 388004)-Net in Base 16 — Upper bound on s

There is no (52, 89, 388005)-net in base 16, because

1 times m-reduction [i] would yield (52, 88, 388005)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9174 214023 560780 911691 257373 608024 183525 981271 180771 682387 062622 856148 202369 272730 289497 837005 362014 911476 > 16⁸⁸ [i]