MinT - Best Known (169, 169+55, s)-Nets in Base 4

Best Known (169, 169+55, s)-Nets in Base 4

(169, 169+55, 1032)-Net over F₄ — Constructive and digital

Digital (169, 224, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 56, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(169, 169+55, 2224)-Net over F₄ — Digital

Digital (169, 224, 2224)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+55, 341843)-Net in Base 4 — Upper bound on s

There is no (169, 224, 341844)-net in base 4, because

1 times m-reduction [i] would yield (169, 223, 341844)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 181 719131 506983 117685 236595 100085 638640 672323 841703 721525 942834 835777 252411 140072 509738 135027 406210 705748 978764 463592 801948 786793 315800 > 4²²³ [i]