MinT - Best Known (72−33, 72, s)-Nets in Base 7

Best Known (72−33, 72, s)-Nets in Base 7

(72−33, 72, 106)-Net over F₇ — Constructive and digital

Digital (39, 72, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 36, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(72−33, 72, 184)-Net over F₇ — Digital

Digital (39, 72, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 36, 92)-net over F₄₉, using
- net from sequence [i] based on digital (3, 91)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
    - a curve from the manYPoints database [i]

(72−33, 72, 6365)-Net in Base 7 — Upper bound on s

There is no (39, 72, 6366)-net in base 7, because

1 times m-reduction [i] would yield (39, 71, 6366)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1 006350 301845 343418 458484 999723 477122 040576 790394 871165 959201 > 7⁷¹ [i]