MinT - Best Known (87−70, 87, s)-Nets in Base 7

Best Known (87−70, 87, s)-Nets in Base 7

(87−70, 87, 25)-Net over F₇ — Constructive and digital

Digital (17, 87, 25)-net over F₇, using

net from sequence [i] based on digital (17, 24)-sequence over F₇, using
- Niederreiter sequence [i]

(87−70, 87, 48)-Net over F₇ — Digital

Digital (17, 87, 48)-net over F₇, using

t-expansion [i] based on digital (13, 87, 48)-net over F₇, using
- net from sequence [i] based on digital (13, 47)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
    - an algebraic function field by Teo [i]

(87−70, 87, 269)-Net in Base 7 — Upper bound on s

There is no (17, 87, 270)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 33 428125 688538 333541 507394 393527 609515 990433 922861 625690 360980 985887 634313 > 7⁸⁷ [i]