Best Known (79, 107, s)-Nets in Base 27
(79, 107, 37960)-Net over F27 — Constructive and digital
Digital (79, 107, 37960)-net over F27, using
- 272 times duplication [i] based on digital (77, 105, 37960)-net over F27, using
- net defined by OOA [i] based on linear OOA(27105, 37960, F27, 28, 28) (dual of [(37960, 28), 1062775, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(27105, 531440, F27, 28) (dual of [531440, 531335, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(27105, 531441, F27, 28) (dual of [531441, 531336, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(27105, 531441, F27, 28) (dual of [531441, 531336, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(27105, 531440, F27, 28) (dual of [531440, 531335, 29]-code), using
- net defined by OOA [i] based on linear OOA(27105, 37960, F27, 28, 28) (dual of [(37960, 28), 1062775, 29]-NRT-code), using
(79, 107, 277881)-Net over F27 — Digital
Digital (79, 107, 277881)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(27107, 277881, F27, 28) (dual of [277881, 277774, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(27107, 531451, F27, 28) (dual of [531451, 531344, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(27105, 531441, F27, 28) (dual of [531441, 531336, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2797, 531441, F27, 25) (dual of [531441, 531344, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(272, 10, F27, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(27107, 531451, F27, 28) (dual of [531451, 531344, 29]-code), using
(79, 107, large)-Net in Base 27 — Upper bound on s
There is no (79, 107, large)-net in base 27, because
- 26 times m-reduction [i] would yield (79, 81, large)-net in base 27, but