Best Known (98−25, 98, s)-Nets in Base 8
(98−25, 98, 682)-Net over F8 — Constructive and digital
Digital (73, 98, 682)-net over F8, using
- net defined by OOA [i] based on linear OOA(898, 682, F8, 25, 25) (dual of [(682, 25), 16952, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(898, 8185, F8, 25) (dual of [8185, 8087, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(898, 8194, F8, 25) (dual of [8194, 8096, 26]-code), using
- trace code [i] based on linear OA(6449, 4097, F64, 25) (dual of [4097, 4048, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- trace code [i] based on linear OA(6449, 4097, F64, 25) (dual of [4097, 4048, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(898, 8194, F8, 25) (dual of [8194, 8096, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(898, 8185, F8, 25) (dual of [8185, 8087, 26]-code), using
(98−25, 98, 814)-Net in Base 8 — Constructive
(73, 98, 814)-net in base 8, using
- trace code for nets [i] based on (24, 49, 407)-net in base 64, using
- base change [i] based on (17, 42, 407)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- (4, 29, 257)-net in base 128, using
- 3 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- base change [i] based on digital (0, 28, 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, 28, 257)-net over F256, using
- 3 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- digital (1, 13, 150)-net over F128, using
- (u, u+v)-construction [i] based on
- base change [i] based on (17, 42, 407)-net in base 128, using
(98−25, 98, 8196)-Net over F8 — Digital
Digital (73, 98, 8196)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(898, 8196, F8, 25) (dual of [8196, 8098, 26]-code), using
- trace code [i] based on linear OA(6449, 4098, F64, 25) (dual of [4098, 4049, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- 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(6447, 4096, F64, 24) (dual of [4096, 4049, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(24) ⊂ Ce(23) [i] based on
- trace code [i] based on linear OA(6449, 4098, F64, 25) (dual of [4098, 4049, 26]-code), using
(98−25, 98, large)-Net in Base 8 — Upper bound on s
There is no (73, 98, large)-net in base 8, because
- 23 times m-reduction [i] would yield (73, 75, large)-net in base 8, but