Best Known (138, 172, s)-Nets in Base 8
(138, 172, 1972)-Net over F8 — Constructive and digital
Digital (138, 172, 1972)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (9, 26, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-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 (9, 26, 45)-net over F8, using
(138, 172, 3856)-Net in Base 8 — Constructive
(138, 172, 3856)-net in base 8, using
- base change [i] based on digital (95, 129, 3856)-net over F16, using
- net defined by OOA [i] based on linear OOA(16129, 3856, F16, 34, 34) (dual of [(3856, 34), 130975, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(16129, 65552, F16, 34) (dual of [65552, 65423, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16129, 65553, F16, 34) (dual of [65553, 65424, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(164, 17, F16, 4) (dual of [17, 13, 5]-code or 17-arc in PG(3,16)), using
- extended Reed–Solomon code RSe(13,16) [i]
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(16129, 65553, F16, 34) (dual of [65553, 65424, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(16129, 65552, F16, 34) (dual of [65552, 65423, 35]-code), using
- net defined by OOA [i] based on linear OOA(16129, 3856, F16, 34, 34) (dual of [(3856, 34), 130975, 35]-NRT-code), using
(138, 172, 95795)-Net over F8 — Digital
Digital (138, 172, 95795)-net over F8, using
(138, 172, large)-Net in Base 8 — Upper bound on s
There is no (138, 172, large)-net in base 8, because
- 32 times m-reduction [i] would yield (138, 140, large)-net in base 8, but