MinT - Best Known (212−50, 212, s)-Nets in Base 4

Best Known (212−50, 212, s)-Nets in Base 4

(212−50, 212, 1040)-Net over F₄ — Constructive and digital

Digital (162, 212, 1040)-net over F₄, using

trace code for nets [i] based on digital (3, 53, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(212−50, 212, 2589)-Net over F₄ — Digital

Digital (162, 212, 2589)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−50, 212, 432466)-Net in Base 4 — Upper bound on s

There is no (162, 212, 432467)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 323196 220288 321309 571399 235911 834129 454977 553621 076289 876599 597771 712694 357369 691939 883852 854096 270964 158308 672198 136232 270928 > 4²¹² [i]