Best Known (96, 96+13, s)-Nets in Base 8
(96, 96+13, 2796265)-Net over F8 — Constructive and digital
Digital (96, 109, 2796265)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 11, 65)-net over F8, using
- base reduction for projective spaces (embedding PG(5,64) in PG(10,8)) for nets [i] based on digital (0, 6, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base reduction for projective spaces (embedding PG(5,64) in PG(10,8)) for nets [i] based on digital (0, 6, 65)-net over F64, using
- digital (85, 98, 2796200)-net over F8, using
- net defined by OOA [i] based on linear OOA(898, 2796200, F8, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(898, 8388601, F8, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(898, 8388602, F8, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
- trace code [i] based on linear OOA(6449, 4194301, F64, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6449, 8388602, F64, 13) (dual of [8388602, 8388553, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- OOA 2-folding [i] based on linear OA(6449, 8388602, F64, 13) (dual of [8388602, 8388553, 14]-code), using
- trace code [i] based on linear OOA(6449, 4194301, F64, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(898, 8388602, F8, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(898, 8388601, F8, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
- net defined by OOA [i] based on linear OOA(898, 2796200, F8, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
- digital (5, 11, 65)-net over F8, using
(96, 96+13, large)-Net over F8 — Digital
Digital (96, 109, large)-net over F8, using
- 3 times m-reduction [i] based on digital (96, 112, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
(96, 96+13, large)-Net in Base 8 — Upper bound on s
There is no (96, 109, large)-net in base 8, because
- 11 times m-reduction [i] would yield (96, 98, large)-net in base 8, but