MinT - Best Known (221−54, 221, s)-Nets in Base 4

Best Known (221−54, 221, s)-Nets in Base 4

(221−54, 221, 1032)-Net over F₄ — Constructive and digital

Digital (167, 221, 1032)-net over F₄, using

4¹ 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]

(221−54, 221, 2250)-Net over F₄ — Digital

Digital (167, 221, 2250)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−54, 221, 308480)-Net in Base 4 — Upper bound on s

There is no (167, 221, 308481)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 357811 002752 339414 117384 848703 616546 674927 664214 794289 175315 574389 323832 632181 666195 759338 455748 428746 730371 678961 689138 433821 509376 > 4²²¹ [i]