MinT - Best Known (18, 18+69, s)-Nets in Base 7

Best Known (18, 18+69, s)-Nets in Base 7

(18, 18+69, 26)-Net over F₇ — Constructive and digital

Digital (18, 87, 26)-net over F₇, using

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

(18, 18+69, 51)-Net over F₇ — Digital

Digital (18, 87, 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+69, 288)-Net in Base 7 — Upper bound on s

There is no (18, 87, 289)-net in base 7, because

1 times m-reduction [i] would yield (18, 86, 289)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 5 314085 788750 563824 647310 974293 426817 123409 499536 737209 365222 462633 743729 > 7⁸⁶ [i]