Best Known (58, 82, s)-Nets in Base 8
(58, 82, 389)-Net over F8 — Constructive and digital
Digital (58, 82, 389)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 20, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (38, 62, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 31, 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, 31, 177)-net over F64, using
- digital (8, 20, 35)-net over F8, using
(58, 82, 576)-Net in Base 8 — Constructive
(58, 82, 576)-net in base 8, using
- t-expansion [i] based on (57, 82, 576)-net in base 8, using
- 2 times m-reduction [i] based on (57, 84, 576)-net in base 8, using
- trace code for nets [i] based on (15, 42, 288)-net in base 64, using
- base change [i] based on digital (9, 36, 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, 36, 288)-net over F128, using
- trace code for nets [i] based on (15, 42, 288)-net in base 64, using
- 2 times m-reduction [i] based on (57, 84, 576)-net in base 8, using
(58, 82, 2245)-Net over F8 — Digital
Digital (58, 82, 2245)-net over F8, using
(58, 82, 1120406)-Net in Base 8 — Upper bound on s
There is no (58, 82, 1120407)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 113 079228 055567 506719 805916 710979 125311 615789 640124 127097 187401 321173 875686 > 882 [i]