MinT - Best Known (222−54, 222, s)-Nets in Base 4

Best Known (222−54, 222, s)-Nets in Base 4

(222−54, 222, 1032)-Net over F₄ — Constructive and digital

Digital (168, 222, 1032)-net over F₄, using

4² times duplication [i] based on digital (166, 220, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 55, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(222−54, 222, 2309)-Net over F₄ — Digital

Digital (168, 222, 2309)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−54, 222, 324733)-Net in Base 4 — Upper bound on s

There is no (168, 222, 324734)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 429193 051832 789410 644077 025792 653866 643988 698921 778420 488644 110541 745224 002191 610017 377553 191954 293349 991881 336666 225769 384136 047110 > 4²²² [i]