MinT - Best Known (57−39, 57, s)-Nets in Base 7

Best Known (57−39, 57, s)-Nets in Base 7

(57−39, 57, 26)-Net over F₇ — Constructive and digital

Digital (18, 57, 26)-net over F₇, using

net from sequence [i] based on digital (18, 25)-sequence over F₇, using
- Niederreiter sequence [i]

(57−39, 57, 51)-Net over F₇ — Digital

Digital (18, 57, 51)-net over F₇, using

net from sequence [i] based on digital (18, 50)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 18 and N(F) ≥ 51, using
  - an algebraic function field by Teo [i]

(57−39, 57, 397)-Net in Base 7 — Upper bound on s

There is no (18, 57, 398)-net in base 7, because

1 times m-reduction [i] would yield (18, 56, 398)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 220641 806220 789417 798922 503332 694947 944940 567209 > 7⁵⁶ [i]