MinT - Best Known (14, 14+16, s)-Nets in Base 7

Best Known (14, 14+16, s)-Nets in Base 7

(14, 14+16, 26)-Net over F₇ — Constructive and digital

Digital (14, 30, 26)-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 (5, 21, 13)-net over F₇, using
  - net from sequence [i] based on digital (5, 12)-sequence over F₇, using
    - Niederreiter sequence [i]

(14, 14+16, 51)-Net over F₇ — Digital

Digital (14, 30, 51)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(14, 14+16, 921)-Net in Base 7 — Upper bound on s

There is no (14, 30, 922)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 22 681410 696167 562241 386385 > 7³⁰ [i]