Best Known (76, 102, s)-Nets in Base 8
(76, 102, 630)-Net over F8 — Constructive and digital
Digital (76, 102, 630)-net over F8, using
- net defined by OOA [i] based on linear OOA(8102, 630, F8, 26, 26) (dual of [(630, 26), 16278, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8102, 8190, F8, 26) (dual of [8190, 8088, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8102, 8192, F8, 26) (dual of [8192, 8090, 27]-code), using
- trace code [i] based on linear OA(6451, 4096, F64, 26) (dual of [4096, 4045, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- trace code [i] based on linear OA(6451, 4096, F64, 26) (dual of [4096, 4045, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8102, 8192, F8, 26) (dual of [8192, 8090, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8102, 8190, F8, 26) (dual of [8190, 8088, 27]-code), using
(76, 102, 772)-Net in Base 8 — Constructive
(76, 102, 772)-net in base 8, using
- (u, u+v)-construction [i] based on
- (19, 32, 258)-net in base 8, using
- trace code for nets [i] based on (3, 16, 129)-net in base 64, using
- 5 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- base change [i] based on digital (0, 18, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 18, 129)-net over F128, using
- 5 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- trace code for nets [i] based on (3, 16, 129)-net in base 64, using
- (44, 70, 514)-net in base 8, using
- trace code for nets [i] based on (9, 35, 257)-net in base 64, using
- 1 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
- base change [i] based on digital (0, 27, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 27, 257)-net over F256, using
- 1 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
- trace code for nets [i] based on (9, 35, 257)-net in base 64, using
- (19, 32, 258)-net in base 8, using
(76, 102, 8196)-Net over F8 — Digital
Digital (76, 102, 8196)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8102, 8196, F8, 26) (dual of [8196, 8094, 27]-code), using
- trace code [i] based on linear OA(6451, 4098, F64, 26) (dual of [4098, 4047, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6451, 4096, F64, 26) (dual of [4096, 4045, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6449, 4096, F64, 25) (dual of [4096, 4047, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- trace code [i] based on linear OA(6451, 4098, F64, 26) (dual of [4098, 4047, 27]-code), using
(76, 102, large)-Net in Base 8 — Upper bound on s
There is no (76, 102, large)-net in base 8, because
- 24 times m-reduction [i] would yield (76, 78, large)-net in base 8, but