Best Known (128, 128+31, s)-Nets in Base 8
(128, 128+31, 2219)-Net over F8 — Constructive and digital
Digital (128, 159, 2219)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 23, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (105, 136, 2184)-net over F8, using
- net defined by OOA [i] based on linear OOA(8136, 2184, F8, 31, 31) (dual of [(2184, 31), 67568, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8136, 32761, F8, 31) (dual of [32761, 32625, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8136, 32761, F8, 31) (dual of [32761, 32625, 32]-code), using
- net defined by OOA [i] based on linear OOA(8136, 2184, F8, 31, 31) (dual of [(2184, 31), 67568, 32]-NRT-code), using
- digital (8, 23, 35)-net over F8, using
(128, 128+31, 4369)-Net in Base 8 — Constructive
(128, 159, 4369)-net in base 8, using
- 83 times duplication [i] based on (125, 156, 4369)-net in base 8, using
- base change [i] based on digital (86, 117, 4369)-net over F16, using
- net defined by OOA [i] based on linear OOA(16117, 4369, F16, 31, 31) (dual of [(4369, 31), 135322, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(16117, 65536, F16, 31) (dual of [65536, 65419, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- OOA 15-folding and stacking with additional row [i] based on linear OA(16117, 65536, F16, 31) (dual of [65536, 65419, 32]-code), using
- net defined by OOA [i] based on linear OOA(16117, 4369, F16, 31, 31) (dual of [(4369, 31), 135322, 32]-NRT-code), using
- base change [i] based on digital (86, 117, 4369)-net over F16, using
(128, 128+31, 105227)-Net over F8 — Digital
Digital (128, 159, 105227)-net over F8, using
(128, 128+31, large)-Net in Base 8 — Upper bound on s
There is no (128, 159, large)-net in base 8, because
- 29 times m-reduction [i] would yield (128, 130, large)-net in base 8, but