Best Known (133, 133+34, s)-Nets in Base 8
(133, 133+34, 1952)-Net over F8 — Constructive and digital
Digital (133, 167, 1952)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 21, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-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 (4, 21, 25)-net over F8, using
(133, 133+34, 3855)-Net in Base 8 — Constructive
(133, 167, 3855)-net in base 8, using
- net defined by OOA [i] based on OOA(8167, 3855, S8, 34, 34), using
- OA 17-folding and stacking [i] based on OA(8167, 65535, S8, 34), using
- discarding factors based on OA(8167, 65540, S8, 34), using
- discarding parts of the base [i] based on linear OA(16125, 65540, F16, 34) (dual of [65540, 65415, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [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(16121, 65536, F16, 33) (dual of [65536, 65415, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(160, 4, F16, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- discarding parts of the base [i] based on linear OA(16125, 65540, F16, 34) (dual of [65540, 65415, 35]-code), using
- discarding factors based on OA(8167, 65540, S8, 34), using
- OA 17-folding and stacking [i] based on OA(8167, 65535, S8, 34), using
(133, 133+34, 69910)-Net over F8 — Digital
Digital (133, 167, 69910)-net over F8, using
(133, 133+34, large)-Net in Base 8 — Upper bound on s
There is no (133, 167, large)-net in base 8, because
- 32 times m-reduction [i] would yield (133, 135, large)-net in base 8, but