MinT - Best Known (54, 54+36, s)-Nets in Base 16

Best Known (54, 54+36, s)-Nets in Base 16

(54, 54+36, 532)-Net over F₁₆ — Constructive and digital

Digital (54, 90, 532)-net over F₁₆, using

trace code for nets [i] based on digital (9, 45, 266)-net over F₂₅₆, using
- net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(54, 54+36, 1175)-Net over F₁₆ — Digital

Digital (54, 90, 1175)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+36, 527996)-Net in Base 16 — Upper bound on s

There is no (54, 90, 527997)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 348612 910201 551332 942151 548374 753280 335533 327191 449230 554507 954751 379657 205946 174273 689958 029050 036697 158466 > 16⁹⁰ [i]