Best Known (135−27, 135, s)-Nets in Base 8
(135−27, 135, 2549)-Net over F8 — Constructive and digital
Digital (108, 135, 2549)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (90, 117, 2521)-net over F8, using
- net defined by OOA [i] based on linear OOA(8117, 2521, F8, 27, 27) (dual of [(2521, 27), 67950, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8117, 32774, F8, 27) (dual of [32774, 32657, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8117, 32779, F8, 27) (dual of [32779, 32662, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8117, 32779, F8, 27) (dual of [32779, 32662, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8117, 32774, F8, 27) (dual of [32774, 32657, 28]-code), using
- net defined by OOA [i] based on linear OOA(8117, 2521, F8, 27, 27) (dual of [(2521, 27), 67950, 28]-NRT-code), using
- digital (5, 18, 28)-net over F8, using
(135−27, 135, 5041)-Net in Base 8 — Constructive
(108, 135, 5041)-net in base 8, using
- net defined by OOA [i] based on OOA(8135, 5041, S8, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(8135, 65534, S8, 27), using
- discarding factors based on OA(8135, 65540, S8, 27), using
- discarding parts of the base [i] based on linear OA(16101, 65540, F16, 27) (dual of [65540, 65439, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- 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(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(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(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(16101, 65540, F16, 27) (dual of [65540, 65439, 28]-code), using
- discarding factors based on OA(8135, 65540, S8, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(8135, 65534, S8, 27), using
(135−27, 135, 73687)-Net over F8 — Digital
Digital (108, 135, 73687)-net over F8, using
(135−27, 135, large)-Net in Base 8 — Upper bound on s
There is no (108, 135, large)-net in base 8, because
- 25 times m-reduction [i] would yield (108, 110, large)-net in base 8, but