Best Known (158−47, 158, s)-Nets in Base 8
(158−47, 158, 1026)-Net over F8 — Constructive and digital
Digital (111, 158, 1026)-net over F8, using
- 8 times m-reduction [i] based on digital (111, 166, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 83, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 83, 513)-net over F64, using
(158−47, 158, 3274)-Net over F8 — Digital
Digital (111, 158, 3274)-net over F8, using
(158−47, 158, 1967550)-Net in Base 8 — Upper bound on s
There is no (111, 158, 1967551)-net in base 8, because
- 1 times m-reduction [i] would yield (111, 157, 1967551)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 6097 207540 474590 139990 544058 447261 102072 505649 025998 183298 076668 399005 427362 050570 941923 855281 812935 064379 189988 582777 869422 870179 704270 188832 > 8157 [i]