MinT - Best Known (115−51, 115, s)-Nets in Base 16

Best Known (115−51, 115, s)-Nets in Base 16

(115−51, 115, 526)-Net over F₁₆ — Constructive and digital

Digital (64, 115, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (64, 116, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 58, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(115−51, 115, 783)-Net over F₁₆ — Digital

Digital (64, 115, 783)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−51, 115, 210035)-Net in Base 16 — Upper bound on s

There is no (64, 115, 210036)-net in base 16, because

1 times m-reduction [i] would yield (64, 114, 210036)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 186074 003966 606215 867469 199979 861246 726737 323509 499296 774308 321454 974459 529996 322359 461140 325374 317380 287992 572616 519619 629443 717296 527876 > 16¹¹⁴ [i]