MinT - Best Known (102−32, 102, s)-Nets in Base 7

Best Known (102−32, 102, s)-Nets in Base 7

(102−32, 102, 206)-Net over F₇ — Constructive and digital

Digital (70, 102, 206)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (18, 34, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 17, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (36, 68, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 34, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(102−32, 102, 1264)-Net over F₇ — Digital

Digital (70, 102, 1264)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−32, 102, 276612)-Net in Base 7 — Upper bound on s

There is no (70, 102, 276613)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 158 495591 682828 419549 977704 214486 419661 401616 585141 807794 767453 956525 851084 578345 262337 > 7¹⁰² [i]