Best Known (131, 131+31, s)-Nets in Base 8
(131, 131+31, 2232)-Net over F8 — Constructive and digital
Digital (131, 162, 2232)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (11, 26, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- digital (105, 136, 2184)-net over F8, using
- net defined by OOA [i] based on linear OOA(8136, 2184, F8, 31, 31) (dual of [(2184, 31), 67568, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8136, 32761, F8, 31) (dual of [32761, 32625, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8136, 32761, F8, 31) (dual of [32761, 32625, 32]-code), using
- net defined by OOA [i] based on linear OOA(8136, 2184, F8, 31, 31) (dual of [(2184, 31), 67568, 32]-NRT-code), using
- digital (11, 26, 48)-net over F8, using
(131, 131+31, 4370)-Net in Base 8 — Constructive
(131, 162, 4370)-net in base 8, using
- 82 times duplication [i] based on (129, 160, 4370)-net in base 8, using
- base change [i] based on digital (89, 120, 4370)-net over F16, using
- net defined by OOA [i] based on linear OOA(16120, 4370, F16, 31, 31) (dual of [(4370, 31), 135350, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(16120, 65551, F16, 31) (dual of [65551, 65431, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16120, 65554, F16, 31) (dual of [65554, 65434, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(16117, 65536, F16, 31) (dual of [65536, 65419, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(16120, 65554, F16, 31) (dual of [65554, 65434, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(16120, 65551, F16, 31) (dual of [65551, 65431, 32]-code), using
- net defined by OOA [i] based on linear OOA(16120, 4370, F16, 31, 31) (dual of [(4370, 31), 135350, 32]-NRT-code), using
- base change [i] based on digital (89, 120, 4370)-net over F16, using
(131, 131+31, 129547)-Net over F8 — Digital
Digital (131, 162, 129547)-net over F8, using
(131, 131+31, large)-Net in Base 8 — Upper bound on s
There is no (131, 162, large)-net in base 8, because
- 29 times m-reduction [i] would yield (131, 133, large)-net in base 8, but