Best Known (76, 76+46, s)-Nets in Base 8
(76, 76+46, 354)-Net over F8 — Constructive and digital
Digital (76, 122, 354)-net over F8, using
- 16 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+46, 432)-Net in Base 8 — Constructive
(76, 122, 432)-net in base 8, using
- 2 times m-reduction [i] based on (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
- trace code for nets [i] based on (14, 62, 216)-net in base 64, using
(76, 76+46, 726)-Net over F8 — Digital
Digital (76, 122, 726)-net over F8, using
(76, 76+46, 83097)-Net in Base 8 — Upper bound on s
There is no (76, 122, 83098)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 150 335173 697049 381862 385399 631540 118673 002380 712698 143089 959597 470058 755958 723840 746612 375072 199900 470586 256436 > 8122 [i]