Best Known (84−24, 84, s)-Nets in Base 8
(84−24, 84, 416)-Net over F8 — Constructive and digital
Digital (60, 84, 416)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (18, 30, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 15, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 15, 104)-net over F64, using
- digital (30, 54, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 27, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64 (see above)
- trace code for nets [i] based on digital (3, 27, 104)-net over F64, using
- digital (18, 30, 208)-net over F8, using
(84−24, 84, 576)-Net in Base 8 — Constructive
(60, 84, 576)-net in base 8, using
- 4 times m-reduction [i] based on (60, 88, 576)-net in base 8, using
- trace code for nets [i] based on (16, 44, 288)-net in base 64, using
- 5 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 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, 42, 288)-net over F128, using
- 5 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- trace code for nets [i] based on (16, 44, 288)-net in base 64, using
(84−24, 84, 3290)-Net over F8 — Digital
Digital (60, 84, 3290)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(884, 3290, F8, 24) (dual of [3290, 3206, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(884, 4095, F8, 24) (dual of [4095, 4011, 25]-code), using
- 1 times truncation [i] based on linear OA(885, 4096, F8, 25) (dual of [4096, 4011, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 1 times truncation [i] based on linear OA(885, 4096, F8, 25) (dual of [4096, 4011, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(884, 4095, F8, 24) (dual of [4095, 4011, 25]-code), using
(84−24, 84, 1584496)-Net in Base 8 — Upper bound on s
There is no (60, 84, 1584497)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 7237 028775 322376 165100 365498 501625 736421 733329 678642 869492 625440 265343 226516 > 884 [i]