Best Known (62, 62+40, s)-Nets in Base 8
(62, 62+40, 354)-Net over F8 — Constructive and digital
Digital (62, 102, 354)-net over F8, using
- 8 times m-reduction [i] based on digital (62, 110, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 55, 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, 55, 177)-net over F64, using
(62, 62+40, 384)-Net in Base 8 — Constructive
(62, 102, 384)-net in base 8, using
- trace code for nets [i] based on (11, 51, 192)-net in base 64, using
- 5 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 48, 192)-net over F128, using
- 5 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
(62, 62+40, 519)-Net over F8 — Digital
Digital (62, 102, 519)-net over F8, using
(62, 62+40, 47847)-Net in Base 8 — Upper bound on s
There is no (62, 102, 47848)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 130 423155 742225 214760 434117 977123 122927 754761 744514 011972 107202 123011 809039 032984 616997 937766 > 8102 [i]