MinT - Best Known (220−54, 220, s)-Nets in Base 4

Best Known (220−54, 220, s)-Nets in Base 4

(220−54, 220, 1032)-Net over F₄ — Constructive and digital

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]

(220−54, 220, 2193)-Net over F₄ — Digital

Digital (166, 220, 2193)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−54, 220, 293040)-Net in Base 4 — Upper bound on s

There is no (166, 220, 293041)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 839473 495066 875765 468187 356967 986026 153354 707236 292420 964550 298711 058752 017362 989595 027182 974302 237178 372826 454644 289290 134468 294752 > 4²²⁰ [i]