Best Known (76, 76+48, s)-Nets in Base 8
(76, 76+48, 354)-Net over F8 — Constructive and digital
Digital (76, 124, 354)-net over F8, using
- 14 times m-reduction [i] based on digital (76, 138, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 69, 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, 69, 177)-net over F64, using
(76, 76+48, 432)-Net in Base 8 — Constructive
(76, 124, 432)-net in base 8, using
- trace code for nets [i] based on (14, 62, 216)-net in base 64, using
- 1 times m-reduction [i] based on (14, 63, 216)-net in base 64, using
- base change [i] based on digital (5, 54, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 54, 216)-net over F128, using
- 1 times m-reduction [i] based on (14, 63, 216)-net in base 64, using
(76, 76+48, 643)-Net over F8 — Digital
Digital (76, 124, 643)-net over F8, using
(76, 76+48, 64882)-Net in Base 8 — Upper bound on s
There is no (76, 124, 64883)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 9620 267802 189842 808851 380487 306804 046640 326788 391482 774485 152699 209885 273486 001286 159386 420951 404340 902670 699028 > 8124 [i]