MinT - Best Known (111−50, 111, s)-Nets in Base 16

Best Known (111−50, 111, s)-Nets in Base 16

(111−50, 111, 524)-Net over F₁₆ — Constructive and digital

Digital (61, 111, 524)-net over F₁₆, using

1 times m-reduction [i] based on digital (61, 112, 524)-net over F₁₆, using
- trace code for nets [i] based on digital (5, 56, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(111−50, 111, 695)-Net over F₁₆ — Digital

Digital (61, 111, 695)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−50, 111, 150587)-Net in Base 16 — Upper bound on s

There is no (61, 111, 150588)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 45 433921 944843 723651 634389 749166 760768 278432 006837 224804 353550 372790 847925 698700 861194 964811 369368 551111 352769 623708 439430 878905 144251 > 16¹¹¹ [i]