Best Known (19−15, 19, s)-Nets in Base 7
(19−15, 19, 12)-Net over F7 — Constructive and digital
Digital (4, 19, 12)-net over F7, using
- net from sequence [i] based on digital (4, 11)-sequence over F7, using
- Niederreiter sequence (Bratley–Fox–Niederreiter implementation) with equidistant coordinate [i]
(19−15, 19, 24)-Net over F7 — Digital
Digital (4, 19, 24)-net over F7, using
- net from sequence [i] based on digital (4, 23)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 4 and N(F) ≥ 24, using
(19−15, 19, 79)-Net in Base 7 — Upper bound on s
There is no (4, 19, 80)-net in base 7, because
- 1 times m-reduction [i] would yield (4, 18, 80)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 1652 113838 545537 > 718 [i]