MinT - Best Known (50, 50+41, s)-Nets in Base 7

Best Known (50, 50+41, s)-Nets in Base 7

(50, 50+41, 108)-Net over F₇ — Constructive and digital

Digital (50, 91, 108)-net over F₇, using

1 times m-reduction [i] based on digital (50, 92, 108)-net over F₇, using
- trace code for nets [i] based on digital (4, 46, 54)-net over F₄₉, using
  - net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(50, 50+41, 211)-Net over F₇ — Digital

Digital (50, 91, 211)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+41, 8779)-Net in Base 7 — Upper bound on s

There is no (50, 91, 8780)-net in base 7, because

1 times m-reduction [i] would yield (50, 90, 8780)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 11467 564761 160124 241225 336189 932813 109933 027273 707388 019084 653099 611503 156801 > 7⁹⁰ [i]