MinT - Best Known (218−53, 218, s)-Nets in Base 4

Best Known (218−53, 218, s)-Nets in Base 4

(218−53, 218, 1032)-Net over F₄ — Constructive and digital

Digital (165, 218, 1032)-net over F₄, using

4² times duplication [i] based on digital (163, 216, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 54, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(218−53, 218, 2279)-Net over F₄ — Digital

Digital (165, 218, 2279)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−53, 218, 372419)-Net in Base 4 — Upper bound on s

There is no (165, 218, 372420)-net in base 4, because

1 times m-reduction [i] would yield (165, 217, 372420)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44364 257794 268475 441933 253653 871322 201942 181540 166269 566564 257819 938511 334567 336209 172239 952015 830000 950944 880360 743225 920727 256232 > 4²¹⁷ [i]