Best Known (137, 137+34, s)-Nets in Base 8
(137, 137+34, 1962)-Net over F8 — Constructive and digital
Digital (137, 171, 1962)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 25, 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 (112, 146, 1927)-net over F8, using
- net defined by OOA [i] based on linear OOA(8146, 1927, F8, 34, 34) (dual of [(1927, 34), 65372, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(8146, 32759, F8, 34) (dual of [32759, 32613, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(8146, 32759, F8, 34) (dual of [32759, 32613, 35]-code), using
- net defined by OOA [i] based on linear OOA(8146, 1927, F8, 34, 34) (dual of [(1927, 34), 65372, 35]-NRT-code), using
- digital (8, 25, 35)-net over F8, using
(137, 137+34, 3855)-Net in Base 8 — Constructive
(137, 171, 3855)-net in base 8, using
- 1 times m-reduction [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
(137, 137+34, 89946)-Net over F8 — Digital
Digital (137, 171, 89946)-net over F8, using
(137, 137+34, large)-Net in Base 8 — Upper bound on s
There is no (137, 171, large)-net in base 8, because
- 32 times m-reduction [i] would yield (137, 139, large)-net in base 8, but