MinT - Best Known (23, 48, s)-Nets in Base 7

Best Known (23, 48, s)-Nets in Base 7

(23, 48, 31)-Net over F₇ — Constructive and digital

Digital (23, 48, 31)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (1, 13, 13)-net over F₇, using
  - a shift-net [i]
2. digital (10, 35, 18)-net over F₇, using
  - net from sequence [i] based on digital (10, 17)-sequence over F₇, using
    - Niederreiter sequence [i]

(23, 48, 75)-Net over F₇ — Digital

Digital (23, 48, 75)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(23, 48, 1792)-Net in Base 7 — Upper bound on s

There is no (23, 48, 1793)-net in base 7, because

1 times m-reduction [i] would yield (23, 47, 1793)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 5274 306816 444354 231072 298723 858293 305377 > 7⁴⁷ [i]