MinT - Best Known (227−54, 227, s)-Nets in Base 4

Best Known (227−54, 227, s)-Nets in Base 4

(227−54, 227, 1036)-Net over F₄ — Constructive and digital

Digital (173, 227, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (173, 228, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 57, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(227−54, 227, 2628)-Net over F₄ — Digital

Digital (173, 227, 2628)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−54, 227, 419784)-Net in Base 4 — Upper bound on s

There is no (173, 227, 419785)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46519 209130 832754 225592 550688 741698 262741 744609 561044 486778 974996 898803 373744 033065 480251 158110 063197 241205 518370 915950 567596 910933 666752 > 4²²⁷ [i]