MinT - Best Known (65, 94, s)-Nets in Base 7

Best Known (65, 94, s)-Nets in Base 7

(65, 94, 208)-Net over F₇ — Constructive and digital

Digital (65, 94, 208)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (18, 32, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 16, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (33, 62, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 31, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(65, 94, 1308)-Net over F₇ — Digital

Digital (65, 94, 1308)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 94, 414154)-Net in Base 7 — Upper bound on s

There is no (65, 94, 414155)-net in base 7, because

1 times m-reduction [i] would yield (65, 93, 414155)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 927530 401620 502231 307891 310165 143618 406686 248942 840449 337175 601342 091707 529669 > 7⁹³ [i]