Best Known (103, 103+40, s)-Nets in Base 8
(103, 103+40, 1026)-Net over F8 — Constructive and digital
Digital (103, 143, 1026)-net over F8, using
- 7 times m-reduction [i] based on digital (103, 150, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 75, 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
- trace code for nets [i] based on digital (28, 75, 513)-net over F64, using
(103, 103+40, 4526)-Net over F8 — Digital
Digital (103, 143, 4526)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8143, 4526, F8, 40) (dual of [4526, 4383, 41]-code), using
- 428 step Varšamov–Edel lengthening with (ri) = (1, 53 times 0, 1, 153 times 0, 1, 219 times 0) [i] based on linear OA(8140, 4095, F8, 40) (dual of [4095, 3955, 41]-code), using
- 1 times truncation [i] based on linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using
- an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- 1 times truncation [i] based on linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using
- 428 step Varšamov–Edel lengthening with (ri) = (1, 53 times 0, 1, 153 times 0, 1, 219 times 0) [i] based on linear OA(8140, 4095, F8, 40) (dual of [4095, 3955, 41]-code), using
(103, 103+40, 3398599)-Net in Base 8 — Upper bound on s
There is no (103, 143, 3398600)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1386 337038 279628 362455 111104 361480 947154 014619 478223 617265 822734 325436 947461 525300 970477 313129 084573 297032 209484 141390 323996 704636 > 8143 [i]