MinT - Best Known (81−47, 81, s)-Nets in Base 7

Best Known (81−47, 81, s)-Nets in Base 7

(81−47, 81, 35)-Net over F₇ — Constructive and digital

Digital (34, 81, 35)-net over F₇, using

t-expansion [i] based on digital (33, 81, 35)-net over F₇, using
- net from sequence [i] based on digital (33, 34)-sequence over F₇, using
  - Niederreiter sequence [i]

(81−47, 81, 96)-Net over F₇ — Digital

Digital (34, 81, 96)-net over F₇, using

t-expansion [i] based on digital (33, 81, 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]

(81−47, 81, 1352)-Net in Base 7 — Upper bound on s

There is no (34, 81, 1353)-net in base 7, because

1 times m-reduction [i] would yield (34, 80, 1353)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 41 055297 109122 480930 361175 033411 272321 720851 002937 973769 658276 799543 > 7⁸⁰ [i]