MinT - Best Known (64−28, 64, s)-Nets in Base 7

Best Known (64−28, 64, s)-Nets in Base 7

(64−28, 64, 108)-Net over F₇ — Constructive and digital

Digital (36, 64, 108)-net over F₇, using

trace code for nets [i] based on digital (4, 32, 54)-net over F₄₉, using
- net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(64−28, 64, 185)-Net over F₇ — Digital

Digital (36, 64, 185)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(7⁶⁴, 185, F₇, 2, 28) (dual of [(185, 2), 306, 29]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(7⁶², 184, F₇, 2, 28) (dual of [(184, 2), 306, 29]-NRT-code), using
  - extracting embedded OOA [i] based on digital (34, 62, 184)-net over F₇, using
    - trace code for nets [i] based on digital (3, 31, 92)-net over F₄₉, using
      - net from sequence [i] based on digital (3, 91)-sequence over F₄₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
        a curve from the manYPoints database [i]

(64−28, 64, 7346)-Net in Base 7 — Upper bound on s

There is no (36, 64, 7347)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1 220541 585425 990043 141460 009810 795891 069175 616405 173653 > 7⁶⁴ [i]