MinT - Best Known (34, 34+76, s)-Nets in Base 7

Best Known (34, 34+76, s)-Nets in Base 7

(34, 34+76, 35)-Net over F₇ — Constructive and digital

Digital (34, 110, 35)-net over F₇, using

t-expansion [i] based on digital (33, 110, 35)-net over F₇, using
- net from sequence [i] based on digital (33, 34)-sequence over F₇, using
  - Niederreiter sequence [i]

(34, 34+76, 96)-Net over F₇ — Digital

Digital (34, 110, 96)-net over F₇, using

t-expansion [i] based on digital (33, 110, 96)-net over F₇, using
- net from sequence [i] based on digital (33, 95)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 33 and N(F) ≥ 96, using
    - an algebraic function field by Teo [i]

(34, 34+76, 675)-Net in Base 7 — Upper bound on s

There is no (34, 110, 676)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 950 762908 426466 209798 894295 877385 822617 852537 401804 818207 289412 918511 354423 931503 940325 736633 > 7¹¹⁰ [i]