MinT - Best Known (70, 70+31, s)-Nets in Base 7

Best Known (70, 70+31, s)-Nets in Base 7

(70, 70+31, 208)-Net over F₇ — Constructive and digital

Digital (70, 101, 208)-net over F₇, using

7¹ times duplication [i] based on digital (69, 100, 208)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (19, 34, 104)-net over F₇, using
    - trace code for nets [i] based on digital (2, 17, 52)-net over F₄₉, using
      - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (35, 66, 104)-net over F₇, using
    - trace code for nets [i] based on digital (2, 33, 52)-net over F₄₉, using
      - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(70, 70+31, 1420)-Net over F₇ — Digital

Digital (70, 101, 1420)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+31, 460885)-Net in Base 7 — Upper bound on s

There is no (70, 101, 460886)-net in base 7, because

1 times m-reduction [i] would yield (70, 100, 460886)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 234492 598821 548828 613239 416342 476522 159920 751305 173670 387737 170218 090137 875403 457233 > 7¹⁰⁰ [i]