MinT - Best Known (15, 15+69, s)-Nets in Base 7

Best Known (15, 15+69, s)-Nets in Base 7

(15, 15+69, 23)-Net over F₇ — Constructive and digital

Digital (15, 84, 23)-net over F₇, using

net from sequence [i] based on digital (15, 22)-sequence over F₇, using
- Niederreiter sequence [i]

(15, 15+69, 48)-Net over F₇ — Digital

Digital (15, 84, 48)-net over F₇, using

t-expansion [i] based on digital (13, 84, 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]

(15, 15+69, 239)-Net in Base 7 — Upper bound on s

There is no (15, 84, 240)-net in base 7, because

1 times m-reduction [i] would yield (15, 83, 240)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 15343 149427 259032 930240 762966 693161 679703 382765 615542 533811 970529 409569 > 7⁸³ [i]