MinT - Best Known (67, 101, s)-Nets in Base 7

Best Known (67, 101, s)-Nets in Base 7

(67, 101, 150)-Net over F₇ — Constructive and digital

Digital (67, 101, 150)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (16, 33, 50)-net over F₇, using
  - base reduction for projective spaces (embedding PG(16,49) in PG(32,7)) for nets [i] based on digital (0, 17, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
        the rational function field F₄₉(x) [i]
      - Niederreiter sequence [i]
2. digital (34, 68, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 34, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(67, 101, 863)-Net over F₇ — Digital

Digital (67, 101, 863)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 101, 125496)-Net in Base 7 — Upper bound on s

There is no (67, 101, 125497)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 22 641587 452422 593094 533172 546618 354983 573843 755505 618839 276970 586627 165802 810176 831703 > 7¹⁰¹ [i]