Best Known (97, 97+27, s)-Nets in Base 8
(97, 97+27, 2523)-Net over F8 — Constructive and digital
Digital (97, 124, 2523)-net over F8, using
- 81 times duplication [i] based on digital (96, 123, 2523)-net over F8, using
- net defined by OOA [i] based on linear OOA(8123, 2523, F8, 27, 27) (dual of [(2523, 27), 67998, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8123, 32800, F8, 27) (dual of [32800, 32677, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [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(891, 32768, F8, 21) (dual of [32768, 32677, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- OOA 13-folding and stacking with additional row [i] based on linear OA(8123, 32800, F8, 27) (dual of [32800, 32677, 28]-code), using
- net defined by OOA [i] based on linear OOA(8123, 2523, F8, 27, 27) (dual of [(2523, 27), 67998, 28]-NRT-code), using
(97, 97+27, 32802)-Net over F8 — Digital
Digital (97, 124, 32802)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8124, 32802, F8, 27) (dual of [32802, 32678, 28]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8123, 32800, F8, 27) (dual of [32800, 32677, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [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(891, 32768, F8, 21) (dual of [32768, 32677, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(8123, 32801, F8, 26) (dual of [32801, 32678, 27]-code), using Gilbert–Varšamov bound and bm = 8123 > Vbs−1(k−1) = 6 756558 548437 068382 526976 464058 897478 129237 677429 614553 314672 449596 518943 457230 515123 661988 166514 954872 257255 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 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
- linear OA(8123, 32800, F8, 27) (dual of [32800, 32677, 28]-code), using
- construction X with Varšamov bound [i] based on
(97, 97+27, large)-Net in Base 8 — Upper bound on s
There is no (97, 124, large)-net in base 8, because
- 25 times m-reduction [i] would yield (97, 99, large)-net in base 8, but