MinT - Best Known (52, 52+47, s)-Nets in Base 7

Best Known (52, 52+47, s)-Nets in Base 7

(52, 52+47, 104)-Net over F₇ — Constructive and digital

Digital (52, 99, 104)-net over F₇, using

1 times m-reduction [i] based on digital (52, 100, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 50, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(52, 52+47, 184)-Net over F₇ — Digital

Digital (52, 99, 184)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+47, 6253)-Net in Base 7 — Upper bound on s

There is no (52, 99, 6254)-net in base 7, because

1 times m-reduction [i] would yield (52, 98, 6254)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 66109 046846 920457 847119 863830 922541 465327 657474 376321 571511 724820 679576 196348 210433 > 7⁹⁸ [i]