Best Known (51, 51+32, s)-Nets in Base 8
(51, 51+32, 354)-Net over F8 — Constructive and digital
Digital (51, 83, 354)-net over F8, using
- 5 times m-reduction [i] based on digital (51, 88, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 44, 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, 44, 177)-net over F64, using
(51, 51+32, 384)-Net in Base 8 — Constructive
(51, 83, 384)-net in base 8, using
- 1 times m-reduction [i] based on (51, 84, 384)-net in base 8, using
- trace code for nets [i] based on (9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 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, 36, 192)-net over F128, using
- trace code for nets [i] based on (9, 42, 192)-net in base 64, using
(51, 51+32, 480)-Net over F8 — Digital
Digital (51, 83, 480)-net over F8, using
(51, 51+32, 47003)-Net in Base 8 — Upper bound on s
There is no (51, 83, 47004)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 904 799865 892249 806046 388772 365816 133874 388773 072806 087429 049324 652240 616383 > 883 [i]