MinT - Best Known (15, 15+16, s)-Nets in Base 7

Best Known (15, 15+16, s)-Nets in Base 7

(15, 15+16, 50)-Net over F₇ — Constructive and digital

Digital (15, 31, 50)-net over F₇, using

base reduction for projective spaces (embedding PG(15,49) in PG(30,7)) for nets [i] based on digital (0, 16, 50)-net over F₄₉, using
- net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
    - the rational function field F₄₉(x) [i]
  - Niederreiter sequence [i]

(15, 15+16, 60)-Net over F₇ — Digital

Digital (15, 31, 60)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(15, 15+16, 1176)-Net in Base 7 — Upper bound on s

There is no (15, 31, 1177)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 158 532868 255454 098383 324865 > 7³¹ [i]