MinT - Best Known (34, 34+70, s)-Nets in Base 7

Best Known (34, 34+70, s)-Nets in Base 7

(34, 34+70, 35)-Net over F₇ — Constructive and digital

Digital (34, 104, 35)-net over F₇, using

t-expansion [i] based on digital (33, 104, 35)-net over F₇, using
- net from sequence [i] based on digital (33, 34)-sequence over F₇, using
  - Niederreiter sequence [i]

(34, 34+70, 96)-Net over F₇ — Digital

Digital (34, 104, 96)-net over F₇, using

t-expansion [i] based on digital (33, 104, 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+70, 729)-Net in Base 7 — Upper bound on s

There is no (34, 104, 730)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7963 551088 260250 974736 336733 319578 067741 141424 518786 426882 961838 704254 004385 992082 630089 > 7¹⁰⁴ [i]