MinT - Best Known (18, 18+53, s)-Nets in Base 7

Best Known (18, 18+53, s)-Nets in Base 7

(18, 18+53, 26)-Net over F₇ — Constructive and digital

Digital (18, 71, 26)-net over F₇, using

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

(18, 18+53, 51)-Net over F₇ — Digital

Digital (18, 71, 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]

(18, 18+53, 314)-Net in Base 7 — Upper bound on s

There is no (18, 71, 315)-net in base 7, because

1 times m-reduction [i] would yield (18, 70, 315)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 144896 441275 567452 917278 011720 799809 782215 735947 031836 572509 > 7⁷⁰ [i]