MinT - Best Known (34, 34+73, s)-Nets in Base 7

Best Known (34, 34+73, s)-Nets in Base 7

(34, 34+73, 35)-Net over F₇ — Constructive and digital

Digital (34, 107, 35)-net over F₇, using

t-expansion [i] based on digital (33, 107, 35)-net over F₇, using
- net from sequence [i] based on digital (33, 34)-sequence over F₇, using
  - Niederreiter sequence [i]

(34, 34+73, 96)-Net over F₇ — Digital

Digital (34, 107, 96)-net over F₇, using

t-expansion [i] based on digital (33, 107, 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+73, 709)-Net in Base 7 — Upper bound on s

There is no (34, 107, 710)-net in base 7, because

1 times m-reduction [i] would yield (34, 106, 710)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 391070 638239 757698 404203 112389 389408 199279 495140 882644 456624 502894 243709 984698 156845 989225 > 7¹⁰⁶ [i]