MinT - Best Known (73, 73+35, s)-Nets in Base 7

Best Known (73, 73+35, s)-Nets in Base 7

(73, 73+35, 204)-Net over F₇ — Constructive and digital

Digital (73, 108, 204)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (19, 36, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 18, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (37, 72, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 36, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(73, 73+35, 1108)-Net over F₇ — Digital

Digital (73, 108, 1108)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+35, 249414)-Net in Base 7 — Upper bound on s

There is no (73, 108, 249415)-net in base 7, because

1 times m-reduction [i] would yield (73, 107, 249415)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2 663833 514759 545735 632502 044415 217672 631423 169291 843803 212070 982598 681081 812883 541830 096203 > 7¹⁰⁷ [i]