MinT - Best Known (252−62, 252, s)-Nets in Base 4

Best Known (252−62, 252, s)-Nets in Base 4

(252−62, 252, 1032)-Net over F₄ — Constructive and digital

Digital (190, 252, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 63, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(252−62, 252, 2442)-Net over F₄ — Digital

Digital (190, 252, 2442)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−62, 252, 324371)-Net in Base 4 — Upper bound on s

There is no (190, 252, 324372)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 376037 183773 719362 657245 066332 718265 609445 666461 595004 400875 136772 062526 601371 172328 364972 371404 067458 564656 685830 494467 365304 304873 881866 051647 368512 > 4²⁵² [i]