MinT - Best Known (211−51, 211, s)-Nets in Base 4

Best Known (211−51, 211, s)-Nets in Base 4

(211−51, 211, 1032)-Net over F₄ — Constructive and digital

Digital (160, 211, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (160, 212, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 53, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(211−51, 211, 2280)-Net over F₄ — Digital

Digital (160, 211, 2280)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−51, 211, 387066)-Net in Base 4 — Upper bound on s

There is no (160, 211, 387067)-net in base 4, because

1 times m-reduction [i] would yield (160, 210, 387067)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 707756 959401 962230 698834 227949 420198 125493 380234 373614 033246 516035 355716 637834 930771 084485 029861 522712 687753 048747 456996 871150 > 4²¹⁰ [i]