MinT - Best Known (86−26, 86, s)-Nets in Base 7

Best Known (86−26, 86, s)-Nets in Base 7

(86−26, 86, 208)-Net over F₇ — Constructive and digital

Digital (60, 86, 208)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (17, 30, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 15, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (30, 56, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 28, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(86−26, 86, 1382)-Net over F₇ — Digital

Digital (60, 86, 1382)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−26, 86, 368039)-Net in Base 7 — Upper bound on s

There is no (60, 86, 368040)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 4 769210 609889 954578 823115 164997 624364 776510 121190 154249 205633 907475 416433 > 7⁸⁶ [i]