Best Known (135−40, 135, s)-Nets in Base 8
(135−40, 135, 513)-Net over F8 — Constructive and digital
Digital (95, 135, 513)-net over F8, using
- base reduction for projective spaces (embedding PG(67,64) in PG(134,8)) for nets [i] based on digital (28, 68, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(135−40, 135, 576)-Net in Base 8 — Constructive
(95, 135, 576)-net in base 8, using
- 15 times m-reduction [i] based on (95, 150, 576)-net in base 8, using
- trace code for nets [i] based on (20, 75, 288)-net in base 64, using
- 2 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 66, 288)-net over F128, using
- 2 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- trace code for nets [i] based on (20, 75, 288)-net in base 64, using
(135−40, 135, 2960)-Net over F8 — Digital
Digital (95, 135, 2960)-net over F8, using
(135−40, 135, 1479319)-Net in Base 8 — Upper bound on s
There is no (95, 135, 1479320)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 82 632580 437831 058060 043852 188429 336917 392359 736687 943677 765397 149367 655141 733942 702892 485942 361585 182772 764505 037483 362163 > 8135 [i]