Best Known (15, 84, s)-Nets in Base 8
(15, 84, 65)-Net over F8 — Constructive and digital
Digital (15, 84, 65)-net over F8, using
- t-expansion [i] based on digital (14, 84, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(15, 84, 288)-Net in Base 8 — Upper bound on s
There is no (15, 84, 289)-net in base 8, because
- 1 times m-reduction [i] would yield (15, 83, 289)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 923 828058 456078 431663 043601 331215 967509 022191 809982 018297 525986 942575 302080 > 883 [i]