Best Known (62, 62+38, s)-Nets in Base 8
(62, 62+38, 354)-Net over F8 — Constructive and digital
Digital (62, 100, 354)-net over F8, using
- 10 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+38, 384)-Net in Base 8 — Constructive
(62, 100, 384)-net in base 8, using
- 2 times m-reduction [i] based on (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
- trace code for nets [i] based on (11, 51, 192)-net in base 64, using
(62, 62+38, 596)-Net over F8 — Digital
Digital (62, 100, 596)-net over F8, using
(62, 62+38, 64142)-Net in Base 8 — Upper bound on s
There is no (62, 100, 64143)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2 037562 698325 368356 810475 108818 022044 269860 431381 455836 079133 174439 065249 563786 497067 835360 > 8100 [i]