MinT - Best Known (52, 52+41, s)-Nets in Base 7

Best Known (52, 52+41, s)-Nets in Base 7

(52, 52+41, 110)-Net over F₇ — Constructive and digital

Digital (52, 93, 110)-net over F₇, using

1 times m-reduction [i] based on digital (52, 94, 110)-net over F₇, using
- trace code for nets [i] based on digital (5, 47, 55)-net over F₄₉, using
  - net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(52, 52+41, 234)-Net over F₇ — Digital

Digital (52, 93, 234)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+41, 10668)-Net in Base 7 — Upper bound on s

There is no (52, 93, 10669)-net in base 7, because

1 times m-reduction [i] would yield (52, 92, 10669)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 562098 290339 188321 436655 294077 521837 877180 244162 556817 712271 299909 460206 236257 > 7⁹² [i]