MinT - Best Known (52, 52+49, s)-Nets in Base 7

Best Known (52, 52+49, s)-Nets in Base 7

(52, 52+49, 102)-Net over F₇ — Constructive and digital

Digital (52, 101, 102)-net over F₇, using

1 times m-reduction [i] based on digital (52, 102, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 51, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(52, 52+49, 171)-Net over F₇ — Digital

Digital (52, 101, 171)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+49, 5410)-Net in Base 7 — Upper bound on s

There is no (52, 101, 5411)-net in base 7, because

1 times m-reduction [i] would yield (52, 100, 5411)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 246177 573988 464063 093056 658117 842946 289106 596802 874169 966766 774658 955921 700200 889329 > 7¹⁰⁰ [i]