MinT - Best Known (76−24, 76, s)-Nets in Base 7

Best Known (76−24, 76, s)-Nets in Base 7

(76−24, 76, 204)-Net over F₇ — Constructive and digital

Digital (52, 76, 204)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (14, 26, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 13, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (26, 50, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 25, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(76−24, 76, 986)-Net over F₇ — Digital

Digital (52, 76, 986)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(76−24, 76, 198372)-Net in Base 7 — Upper bound on s

There is no (52, 76, 198373)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 16883 629152 852720 628532 798153 352133 732983 265588 051853 729363 795233 > 7⁷⁶ [i]