MinT - Best Known (73−23, 73, s)-Nets in Base 7

Best Known (73−23, 73, s)-Nets in Base 7

(73−23, 73, 204)-Net over F₇ — Constructive and digital

Digital (50, 73, 204)-net over F₇, using

7¹ times duplication [i] based on digital (49, 72, 204)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 24, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 12, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (25, 48, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 24, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(73−23, 73, 972)-Net over F₇ — Digital

Digital (50, 73, 972)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−23, 73, 278229)-Net in Base 7 — Upper bound on s

There is no (50, 73, 278230)-net in base 7, because

1 times m-reduction [i] would yield (50, 72, 278230)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7 031838 311249 446683 011446 738533 405841 576515 448139 125934 105209 > 7⁷² [i]