MinT - Best Known (57, 57+44, s)-Nets in Base 16

Best Known (57, 57+44, s)-Nets in Base 16

(57, 57+44, 526)-Net over F₁₆ — Constructive and digital

Digital (57, 101, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (57, 102, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 51, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(57, 57+44, 780)-Net over F₁₆ — Digital

Digital (57, 101, 780)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+44, 203583)-Net in Base 16 — Upper bound on s

There is no (57, 101, 203584)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 41 320240 639063 729881 885944 258546 137284 436683 697304 934110 152309 623373 155633 144440 950760 140225 310430 675631 628054 420395 127221 > 16¹⁰¹ [i]