Best Known (108−28, 108, s)-Nets in Base 27
(108−28, 108, 37961)-Net over F27 — Constructive and digital
Digital (80, 108, 37961)-net over F27, using
- net defined by OOA [i] based on linear OOA(27108, 37961, F27, 28, 28) (dual of [(37961, 28), 1062800, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(27108, 531454, F27, 28) (dual of [531454, 531346, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(27108, 531456, F27, 28) (dual of [531456, 531348, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(23) [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(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(273, 15, F27, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(27108, 531456, F27, 28) (dual of [531456, 531348, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(27108, 531454, F27, 28) (dual of [531454, 531346, 29]-code), using
(108−28, 108, 315438)-Net over F27 — Digital
Digital (80, 108, 315438)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(27108, 315438, F27, 28) (dual of [315438, 315330, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(27108, 531456, F27, 28) (dual of [531456, 531348, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(23) [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(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(273, 15, F27, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(27108, 531456, F27, 28) (dual of [531456, 531348, 29]-code), using
(108−28, 108, large)-Net in Base 27 — Upper bound on s
There is no (80, 108, large)-net in base 27, because
- 26 times m-reduction [i] would yield (80, 82, large)-net in base 27, but