Best Known (58, 58+36, s)-Nets in Base 8
(58, 58+36, 354)-Net over F8 — Constructive and digital
Digital (58, 94, 354)-net over F8, using
- 8 times m-reduction [i] based on digital (58, 102, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 51, 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, 51, 177)-net over F64, using
(58, 58+36, 384)-Net in Base 8 — Constructive
(58, 94, 384)-net in base 8, using
- 2 times m-reduction [i] based on (58, 96, 384)-net in base 8, using
- trace code for nets [i] based on (10, 48, 192)-net in base 64, using
- 1 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 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, 42, 192)-net over F128, using
- 1 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- trace code for nets [i] based on (10, 48, 192)-net in base 64, using
(58, 58+36, 547)-Net over F8 — Digital
Digital (58, 94, 547)-net over F8, using
(58, 58+36, 56115)-Net in Base 8 — Upper bound on s
There is no (58, 94, 56116)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 7 771887 184948 194053 948246 767921 900263 066264 593106 911447 511778 951380 948667 890045 415805 > 894 [i]