Best Known (136, 171, s)-Nets in Base 8
(136, 171, 1951)-Net over F8 — Constructive and digital
Digital (136, 171, 1951)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-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 (3, 20, 24)-net over F8, using
(136, 171, 67375)-Net over F8 — Digital
Digital (136, 171, 67375)-net over F8, using
(136, 171, large)-Net in Base 8 — Upper bound on s
There is no (136, 171, large)-net in base 8, because
- 33 times m-reduction [i] would yield (136, 138, large)-net in base 8, but