MinT - Best Known (65, 65+53, s)-Nets in Base 16

Best Known (65, 65+53, s)-Nets in Base 16

(65, 65+53, 526)-Net over F₁₆ — Constructive and digital

Digital (65, 118, 526)-net over F₁₆, using

trace code for nets [i] based on digital (6, 59, 263)-net over F₂₅₆, using
- net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(65, 65+53, 741)-Net over F₁₆ — Digital

Digital (65, 118, 741)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+53, 184377)-Net in Base 16 — Upper bound on s

There is no (65, 118, 184378)-net in base 16, because

1 times m-reduction [i] would yield (65, 117, 184378)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 762 187685 511356 399677 753263 770897 324214 919056 947776 444704 060742 244407 797587 269849 901076 755153 489395 657298 637293 387141 883171 599569 464844 049296 > 16¹¹⁷ [i]