MinT - Best Known (103−42, 103, s)-Nets in Base 16

Best Known (103−42, 103, s)-Nets in Base 16

(103−42, 103, 532)-Net over F₁₆ — Constructive and digital

Digital (61, 103, 532)-net over F₁₆, using

1 times m-reduction [i] based on digital (61, 104, 532)-net over F₁₆, using
- trace code for nets [i] based on digital (9, 52, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(103−42, 103, 1160)-Net over F₁₆ — Digital

Digital (61, 103, 1160)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−42, 103, 465921)-Net in Base 16 — Upper bound on s

There is no (61, 103, 465922)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10577 261509 591021 532256 399940 791495 408685 350719 067014 318481 364619 889130 885859 149388 422517 308107 003183 070600 318344 217895 309056 > 16¹⁰³ [i]