Best Known (49−25, 49, s)-Nets in Base 9
(49−25, 49, 82)-Net over F9 — Constructive and digital
Digital (24, 49, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(24,81) in PG(48,9)) for nets [i] based on digital (0, 25, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(49−25, 49, 106)-Net over F9 — Digital
Digital (24, 49, 106)-net over F9, using
(49−25, 49, 4330)-Net in Base 9 — Upper bound on s
There is no (24, 49, 4331)-net in base 9, because
- 1 times m-reduction [i] would yield (24, 48, 4331)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 6371 082574 900646 986012 290998 730364 805450 080545 > 948 [i]