MinT - Best Known (71, 71+56, s)-Nets in Base 16

Best Known (71, 71+56, s)-Nets in Base 16

(71, 71+56, 528)-Net over F₁₆ — Constructive and digital

Digital (71, 127, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (71, 128, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 64, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(71, 71+56, 875)-Net over F₁₆ — Digital

Digital (71, 127, 875)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+56, 217985)-Net in Base 16 — Upper bound on s

There is no (71, 127, 217986)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 838 054901 898486 801384 423284 858348 569112 642319 708790 179748 799092 835495 156363 997175 776363 887958 031851 898946 143126 881712 988949 640481 476706 113936 546613 843296 > 16¹²⁷ [i]