MinT - Best Known (224−47, 224, s)-Nets in Base 4

Best Known (224−47, 224, s)-Nets in Base 4

(224−47, 224, 1064)-Net over F₄ — Constructive and digital

Digital (177, 224, 1064)-net over F₄, using

trace code for nets [i] based on digital (9, 56, 266)-net over F₂₅₆, using
- net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(224−47, 224, 5150)-Net over F₄ — Digital

Digital (177, 224, 5150)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−47, 224, 2161202)-Net in Base 4 — Upper bound on s

There is no (177, 224, 2161203)-net in base 4, because

1 times m-reduction [i] would yield (177, 223, 2161203)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 181 709914 338650 479380 331097 287045 310768 682572 985942 166276 428448 509406 708147 182945 870359 719304 083274 647758 783745 771136 335885 506190 118080 > 4²²³ [i]