Best Known (21−11, 21, s)-Nets in Base 7
(21−11, 21, 50)-Net over F7 — Constructive and digital
Digital (10, 21, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(10,49) in PG(20,7)) for nets [i] based on digital (0, 11, 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
(21−11, 21, 1039)-Net in Base 7 — Upper bound on s
There is no (10, 21, 1040)-net in base 7, because
- 1 times m-reduction [i] would yield (10, 20, 1040)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 79917 824739 693409 > 720 [i]