MinT - Best Known (221−46, 221, s)-Nets in Base 4

Best Known (221−46, 221, s)-Nets in Base 4

(221−46, 221, 1064)-Net over F₄ — Constructive and digital

Digital (175, 221, 1064)-net over F₄, using

4¹ times duplication [i] based on digital (174, 220, 1064)-net over F₄, using
- trace code for nets [i] based on digital (9, 55, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(221−46, 221, 5341)-Net over F₄ — Digital

Digital (175, 221, 5341)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−46, 221, 1915764)-Net in Base 4 — Upper bound on s

There is no (175, 221, 1915765)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 356987 672498 585599 433095 825567 808995 614006 408255 751131 018878 708875 607525 029876 000432 856465 631760 882058 615076 630467 186345 612096 426336 > 4²²¹ [i]