MinT - Best Known (74, 108, s)-Nets in Base 7

Best Known (74, 108, s)-Nets in Base 7

(74, 108, 206)-Net over F₇ — Constructive and digital

Digital (74, 108, 206)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (19, 36, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 18, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (38, 72, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 36, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(74, 108, 1296)-Net over F₇ — Digital

Digital (74, 108, 1296)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 108, 279663)-Net in Base 7 — Upper bound on s

There is no (74, 108, 279664)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 18 647058 477571 749417 470328 915191 074131 189408 477498 612410 924326 509783 909072 901613 728385 878177 > 7¹⁰⁸ [i]