Best Known (138, 138+35, s)-Nets in Base 8
(138, 138+35, 1955)-Net over F8 — Constructive and digital
Digital (138, 173, 1955)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 22, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (116, 151, 1927)-net over F8, using
- net defined by OOA [i] based on linear OOA(8151, 1927, F8, 35, 35) (dual of [(1927, 35), 67294, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(8151, 32760, F8, 35) (dual of [32760, 32609, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(8151, 32760, F8, 35) (dual of [32760, 32609, 36]-code), using
- net defined by OOA [i] based on linear OOA(8151, 1927, F8, 35, 35) (dual of [(1927, 35), 67294, 36]-NRT-code), using
- digital (5, 22, 28)-net over F8, using
(138, 138+35, 3855)-Net in Base 8 — Constructive
(138, 173, 3855)-net in base 8, using
- 81 times duplication [i] based on (137, 172, 3855)-net in base 8, using
- base change [i] based on digital (94, 129, 3855)-net over F16, using
- net defined by OOA [i] based on linear OOA(16129, 3855, F16, 35, 35) (dual of [(3855, 35), 134796, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(16129, 65536, F16, 35) (dual of [65536, 65407, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- OOA 17-folding and stacking with additional row [i] based on linear OA(16129, 65536, F16, 35) (dual of [65536, 65407, 36]-code), using
- net defined by OOA [i] based on linear OOA(16129, 3855, F16, 35, 35) (dual of [(3855, 35), 134796, 36]-NRT-code), using
- base change [i] based on digital (94, 129, 3855)-net over F16, using
(138, 138+35, 76139)-Net over F8 — Digital
Digital (138, 173, 76139)-net over F8, using
(138, 138+35, large)-Net in Base 8 — Upper bound on s
There is no (138, 173, large)-net in base 8, because
- 33 times m-reduction [i] would yield (138, 140, large)-net in base 8, but