MinT - Best Known (218−52, 218, s)-Nets in Base 4

Best Known (218−52, 218, s)-Nets in Base 4

(218−52, 218, 1036)-Net over F₄ — Constructive and digital

Digital (166, 218, 1036)-net over F₄, using

4² times duplication [i] based on digital (164, 216, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 54, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(218−52, 218, 2504)-Net over F₄ — Digital

Digital (166, 218, 2504)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−52, 218, 392816)-Net in Base 4 — Upper bound on s

There is no (166, 218, 392817)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177455 370805 008980 855409 593115 621184 180191 815264 358963 538767 284913 346751 023156 399390 543664 572489 348210 666803 819347 527509 643137 660880 > 4²¹⁸ [i]