MinT - Best Known (214−51, 214, s)-Nets in Base 4

Best Known (214−51, 214, s)-Nets in Base 4

(214−51, 214, 1036)-Net over F₄ — Constructive and digital

Digital (163, 214, 1036)-net over F₄, using

4² 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]

(214−51, 214, 2476)-Net over F₄ — Digital

Digital (163, 214, 2476)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−51, 214, 457126)-Net in Base 4 — Upper bound on s

There is no (163, 214, 457127)-net in base 4, because

1 times m-reduction [i] would yield (163, 213, 457127)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 173 296762 617290 262101 701150 196756 967693 317091 206424 026407 743194 412801 627645 958126 434291 611606 774359 720404 315967 559288 878043 795704 > 4²¹³ [i]