MinT - Best Known (220−46, 220, s)-Nets in Base 4

Best Known (220−46, 220, s)-Nets in Base 4

(220−46, 220, 1064)-Net over F₄ — Constructive and digital

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]

(220−46, 220, 5180)-Net over F₄ — Digital

Digital (174, 220, 5180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−46, 220, 1803703)-Net in Base 4 — Upper bound on s

There is no (174, 220, 1803704)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 839219 550552 065023 924465 425414 317509 639503 362852 393721 692930 128932 742177 673668 738503 701339 285687 181159 951254 476931 196309 080009 966897 > 4²²⁰ [i]