MinT - Best Known (109−39, 109, s)-Nets in Base 7

Best Known (109−39, 109, s)-Nets in Base 7

(109−39, 109, 130)-Net over F₇ — Constructive and digital

Digital (70, 109, 130)-net over F₇, using

1 times m-reduction [i] based on digital (70, 110, 130)-net over F₇, using
- trace code for nets [i] based on digital (15, 55, 65)-net over F₄₉, using
  - net from sequence [i] based on digital (15, 64)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(109−39, 109, 684)-Net over F₇ — Digital

Digital (70, 109, 684)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−39, 109, 84084)-Net in Base 7 — Upper bound on s

There is no (70, 109, 84085)-net in base 7, because

1 times m-reduction [i] would yield (70, 108, 84085)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 18 647688 185986 502980 030034 296563 583829 157306 075569 786690 926485 856351 491287 086458 361003 998775 > 7¹⁰⁸ [i]