MinT - Best Known (58, 58+26, s)-Nets in Base 7

Best Known (58, 58+26, s)-Nets in Base 7

(58, 58+26, 206)-Net over F₇ — Constructive and digital

Digital (58, 84, 206)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (15, 28, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 14, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-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, using
      - Niederreiter sequence [i]

(58, 58+26, 1185)-Net over F₇ — Digital

Digital (58, 84, 1185)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+26, 272819)-Net in Base 7 — Upper bound on s

There is no (58, 84, 272820)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 97329 747740 325660 906249 819163 507210 205742 095831 734444 343874 794988 535129 > 7⁸⁴ [i]