Best Known (18, 18+19, s)-Nets in Base 7
(18, 18+19, 50)-Net over F7 — Constructive and digital
Digital (18, 37, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(18,49) in PG(36,7)) for nets [i] based on digital (0, 19, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction 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]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
(18, 18+19, 67)-Net over F7 — Digital
Digital (18, 37, 67)-net over F7, using
(18, 18+19, 1654)-Net in Base 7 — Upper bound on s
There is no (18, 37, 1655)-net in base 7, because
- 1 times m-reduction [i] would yield (18, 36, 1655)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 2 665222 740043 570387 752363 936667 > 736 [i]