MinT - Best Known (109−51, 109, s)-Nets in Base 7

Best Known (109−51, 109, s)-Nets in Base 7

(109−51, 109, 106)-Net over F₇ — Constructive and digital

Digital (58, 109, 106)-net over F₇, using

1 times m-reduction [i] based on digital (58, 110, 106)-net over F₇, using
- trace code for nets [i] based on digital (3, 55, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(109−51, 109, 211)-Net over F₇ — Digital

Digital (58, 109, 211)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−51, 109, 7574)-Net in Base 7 — Upper bound on s

There is no (58, 109, 7575)-net in base 7, because

1 times m-reduction [i] would yield (58, 108, 7575)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 18 656615 945923 869098 314215 976601 729338 029226 771961 978937 692882 530053 482309 193188 846438 813179 > 7¹⁰⁸ [i]