MinT - Best Known (213−51, 213, s)-Nets in Base 4

Best Known (213−51, 213, s)-Nets in Base 4

(213−51, 213, 1036)-Net over F₄ — Constructive and digital

Digital (162, 213, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (161, 212, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 53, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(213−51, 213, 2409)-Net over F₄ — Digital

Digital (162, 213, 2409)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−51, 213, 432466)-Net in Base 4 — Upper bound on s

There is no (162, 213, 432467)-net in base 4, because

1 times m-reduction [i] would yield (162, 212, 432467)-net in base 4, but
- 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]