MinT - Best Known (210−50, 210, s)-Nets in Base 4

Best Known (210−50, 210, s)-Nets in Base 4

(210−50, 210, 1036)-Net over F₄ — Constructive and digital

Digital (160, 210, 1036)-net over F₄, using

4² times duplication [i] based on digital (158, 208, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 52, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(210−50, 210, 2448)-Net over F₄ — Digital

Digital (160, 210, 2448)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−50, 210, 387066)-Net in Base 4 — Upper bound on s

There is no (160, 210, 387067)-net in base 4, because

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]