Best Known (131−26, 131, s)-Nets in Base 8
(131−26, 131, 2555)-Net over F8 — Constructive and digital
Digital (105, 131, 2555)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 20, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (85, 111, 2521)-net over F8, using
- net defined by OOA [i] based on linear OOA(8111, 2521, F8, 26, 26) (dual of [(2521, 26), 65435, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8111, 32773, F8, 26) (dual of [32773, 32662, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- OA 13-folding and stacking [i] based on linear OA(8111, 32773, F8, 26) (dual of [32773, 32662, 27]-code), using
- net defined by OOA [i] based on linear OOA(8111, 2521, F8, 26, 26) (dual of [(2521, 26), 65435, 27]-NRT-code), using
- digital (7, 20, 34)-net over F8, using
(131−26, 131, 5041)-Net in Base 8 — Constructive
(105, 131, 5041)-net in base 8, using
- 81 times duplication [i] based on (104, 130, 5041)-net in base 8, using
- net defined by OOA [i] based on OOA(8130, 5041, S8, 26, 26), using
- OA 13-folding and stacking [i] based on OA(8130, 65533, S8, 26), using
- discarding factors based on OA(8130, 65540, S8, 26), using
- discarding parts of the base [i] based on linear OA(1697, 65540, F16, 26) (dual of [65540, 65443, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(1697, 65536, F16, 26) (dual of [65536, 65439, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- discarding parts of the base [i] based on linear OA(1697, 65540, F16, 26) (dual of [65540, 65443, 27]-code), using
- discarding factors based on OA(8130, 65540, S8, 26), using
- OA 13-folding and stacking [i] based on OA(8130, 65533, S8, 26), using
- net defined by OOA [i] based on OOA(8130, 5041, S8, 26, 26), using
(131−26, 131, 78485)-Net over F8 — Digital
Digital (105, 131, 78485)-net over F8, using
(131−26, 131, large)-Net in Base 8 — Upper bound on s
There is no (105, 131, large)-net in base 8, because
- 24 times m-reduction [i] would yield (105, 107, large)-net in base 8, but