Best Known (102, 102+50, s)-Nets in Base 8
(102, 102+50, 402)-Net over F8 — Constructive and digital
Digital (102, 152, 402)-net over F8, using
- t-expansion [i] based on digital (101, 152, 402)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (11, 36, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- digital (65, 116, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 58, 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, 58, 177)-net over F64, using
- digital (11, 36, 48)-net over F8, using
- (u, u+v)-construction [i] based on
(102, 102+50, 576)-Net in Base 8 — Constructive
(102, 152, 576)-net in base 8, using
- 10 times m-reduction [i] based on (102, 162, 576)-net in base 8, using
- trace code for nets [i] based on (21, 81, 288)-net in base 64, using
- 3 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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, 72, 288)-net over F128, using
- 3 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- trace code for nets [i] based on (21, 81, 288)-net in base 64, using
(102, 102+50, 1753)-Net over F8 — Digital
Digital (102, 152, 1753)-net over F8, using
(102, 102+50, 450090)-Net in Base 8 — Upper bound on s
There is no (102, 152, 450091)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 186075 483669 740603 950781 052352 220905 434257 819409 725792 055415 728196 401186 355626 658665 060652 281221 713246 378456 664051 815178 561859 480480 717884 > 8152 [i]