Best Known (49−37, 49, s)-Nets in Base 9
(49−37, 49, 40)-Net over F9 — Constructive and digital
Digital (12, 49, 40)-net over F9, using
- t-expansion [i] based on digital (8, 49, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
(49−37, 49, 56)-Net over F9 — Digital
Digital (12, 49, 56)-net over F9, using
- net from sequence [i] based on digital (12, 55)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 12 and N(F) ≥ 56, using
(49−37, 49, 320)-Net in Base 9 — Upper bound on s
There is no (12, 49, 321)-net in base 9, because
- 1 times m-reduction [i] would yield (12, 48, 321)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 6628 573793 919022 939354 820399 161688 898777 920209 > 948 [i]