MinT - Best Known (57−37, 57, s)-Nets in Base 7

Best Known (57−37, 57, s)-Nets in Base 7

(57−37, 57, 28)-Net over F₇ — Constructive and digital

Digital (20, 57, 28)-net over F₇, using

net from sequence [i] based on digital (20, 27)-sequence over F₇, using
- Niederreiter sequence [i]

(57−37, 57, 54)-Net over F₇ — Digital

Digital (20, 57, 54)-net over F₇, using

t-expansion [i] based on digital (19, 57, 54)-net over F₇, using
- net from sequence [i] based on digital (19, 53)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 19 and N(F) ≥ 54, using
    - an algebraic function field by Teo [i]

(57−37, 57, 524)-Net in Base 7 — Upper bound on s

There is no (20, 57, 525)-net in base 7, because

1 times m-reduction [i] would yield (20, 56, 525)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 214522 729341 127373 893066 624607 036097 663861 471721 > 7⁵⁶ [i]