MinT - Best Known (164, 164+42, s)-Nets in Base 4

Best Known (164, 164+42, s)-Nets in Base 4

(164, 164+42, 1064)-Net over F₄ — Constructive and digital

Digital (164, 206, 1064)-net over F₄, using

4² times duplication [i] based on digital (162, 204, 1064)-net over F₄, using
- trace code for nets [i] based on digital (9, 51, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(164, 164+42, 5719)-Net over F₄ — Digital

Digital (164, 206, 5719)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+42, 2329646)-Net in Base 4 — Upper bound on s

There is no (164, 206, 2329647)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10576 975507 236187 220302 338662 050825 979131 518711 631685 606565 567326 797287 625596 812692 010837 388197 821491 313637 908116 658205 042212 > 4²⁰⁶ [i]