Best Known (124−40, 124, s)-Nets in Base 8
(124−40, 124, 400)-Net over F8 — Constructive and digital
Digital (84, 124, 400)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 30, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- digital (54, 94, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 47, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 47, 177)-net over F64, using
- digital (10, 30, 46)-net over F8, using
(124−40, 124, 576)-Net in Base 8 — Constructive
(84, 124, 576)-net in base 8, using
- 6 times m-reduction [i] based on (84, 130, 576)-net in base 8, using
- trace code for nets [i] based on (19, 65, 288)-net in base 64, using
- 5 times m-reduction [i] based on (19, 70, 288)-net in base 64, using
- base change [i] based on digital (9, 60, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 60, 288)-net over F128, using
- 5 times m-reduction [i] based on (19, 70, 288)-net in base 64, using
- trace code for nets [i] based on (19, 65, 288)-net in base 64, using
(124−40, 124, 1655)-Net over F8 — Digital
Digital (84, 124, 1655)-net over F8, using
(124−40, 124, 471362)-Net in Base 8 — Upper bound on s
There is no (84, 124, 471363)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 9619 968961 043670 582818 764898 842175 709985 838370 177163 318194 104534 241325 216009 000572 058338 360353 144219 541974 400784 > 8124 [i]