Best Known (98−38, 98, s)-Nets in Base 8
(98−38, 98, 354)-Net over F8 — Constructive and digital
Digital (60, 98, 354)-net over F8, using
- 8 times m-reduction [i] based on digital (60, 106, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 53, 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, 53, 177)-net over F64, using
(98−38, 98, 384)-Net in Base 8 — Constructive
(60, 98, 384)-net in base 8, using
- t-expansion [i] based on (59, 98, 384)-net in base 8, using
- trace code for nets [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
- trace code for nets [i] based on (10, 49, 192)-net in base 64, using
(98−38, 98, 534)-Net over F8 — Digital
Digital (60, 98, 534)-net over F8, using
(98−38, 98, 51530)-Net in Base 8 — Upper bound on s
There is no (60, 98, 51531)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 31838 047307 554983 285778 774656 831832 421906 197796 814827 082042 839924 942238 640986 012476 371136 > 898 [i]