MinT - Best Known (15, 32, s)-Nets in Base 7

Best Known (15, 32, s)-Nets in Base 7

(15, 32, 27)-Net over F₇ — Constructive and digital

Digital (15, 32, 27)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (1, 9, 13)-net over F₇, using
  - 4 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
2. digital (6, 23, 14)-net over F₇, using
  - net from sequence [i] based on digital (6, 13)-sequence over F₇, using
    - Niederreiter sequence [i]

(15, 32, 54)-Net over F₇ — Digital

Digital (15, 32, 54)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(15, 32, 1176)-Net in Base 7 — Upper bound on s

There is no (15, 32, 1177)-net in base 7, because

1 times m-reduction [i] would yield (15, 31, 1177)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 158 532868 255454 098383 324865 > 7³¹ [i]