Best Known (142−40, 142, s)-Nets in Base 8
(142−40, 142, 1026)-Net over F8 — Constructive and digital
Digital (102, 142, 1026)-net over F8, using
- 6 times m-reduction [i] based on digital (102, 148, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 74, 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, 74, 513)-net over F64, using
(142−40, 142, 4305)-Net over F8 — Digital
Digital (102, 142, 4305)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8142, 4305, F8, 40) (dual of [4305, 4163, 41]-code), using
- 208 step Varšamov–Edel lengthening with (ri) = (1, 53 times 0, 1, 153 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
- 208 step Varšamov–Edel lengthening with (ri) = (1, 53 times 0, 1, 153 times 0) [i] based on linear OA(8140, 4095, F8, 40) (dual of [4095, 3955, 41]-code), using
(142−40, 142, 3062988)-Net in Base 8 — Upper bound on s
There is no (102, 142, 3062989)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 173 292580 163922 324032 278746 096201 961119 956465 544165 141084 584077 309368 395656 388313 152028 057500 752737 069926 353871 743645 273100 917684 > 8142 [i]