MinT - Best Known (244−55, 244, s)-Nets in Base 4

Best Known (244−55, 244, s)-Nets in Base 4

(244−55, 244, 1052)-Net over F₄ — Constructive and digital

Digital (189, 244, 1052)-net over F₄, using

trace code for nets [i] based on digital (6, 61, 263)-net over F₂₅₆, using
- net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(244−55, 244, 3698)-Net over F₄ — Digital

Digital (189, 244, 3698)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−55, 244, 954586)-Net in Base 4 — Upper bound on s

There is no (189, 244, 954587)-net in base 4, because

1 times m-reduction [i] would yield (189, 243, 954587)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 792990 298513 671477 459240 197927 309801 804030 191288 005414 438763 675329 352967 517082 972823 711065 867742 684957 362940 687057 474863 235608 970736 556465 319100 > 4²⁴³ [i]