MinT - Best Known (254−62, 254, s)-Nets in Base 4

Best Known (254−62, 254, s)-Nets in Base 4

(254−62, 254, 1032)-Net over F₄ — Constructive and digital

Digital (192, 254, 1032)-net over F₄, using

4² times duplication [i] based on 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]

(254−62, 254, 2554)-Net over F₄ — Digital

Digital (192, 254, 2554)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−62, 254, 354722)-Net in Base 4 — Upper bound on s

There is no (192, 254, 354723)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 838 047002 999427 248719 555504 874270 638639 919151 164926 376829 035183 994668 143324 199351 239187 412462 449431 261247 980976 970121 188452 853383 979807 482202 835543 388800 > 4²⁵⁴ [i]