MinT - Best Known (70, 70+30, s)-Nets in Base 7

Best Known (70, 70+30, s)-Nets in Base 7

(70, 70+30, 210)-Net over F₇ — Constructive and digital

Digital (70, 100, 210)-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 (36, 66, 106)-net over F₇, using
  - trace code for nets [i] based on digital (3, 33, 53)-net over F₄₉, using
    - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(70, 70+30, 1611)-Net over F₇ — Digital

Digital (70, 100, 1611)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+30, 460885)-Net in Base 7 — Upper bound on s

There is no (70, 100, 460886)-net in base 7, because

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]