MinT - Best Known (61, 61+29, s)-Nets in Base 7

Best Known (61, 61+29, s)-Nets in Base 7

(61, 61+29, 204)-Net over F₇ — Constructive and digital

Digital (61, 90, 204)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (16, 30, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 15, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (31, 60, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 30, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(61, 61+29, 994)-Net over F₇ — Digital

Digital (61, 90, 994)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+29, 237519)-Net in Base 7 — Upper bound on s

There is no (61, 90, 237520)-net in base 7, because

1 times m-reduction [i] would yield (61, 89, 237520)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1635 828797 744218 540095 881734 187526 077119 376187 295308 361841 403807 867999 255649 > 7⁸⁹ [i]