Best Known (90, 106, s)-Nets in Base 27
(90, 106, 1181437)-Net over F27 — Constructive and digital
Digital (90, 106, 1181437)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (22, 30, 132862)-net over F27, using
- net defined by OOA [i] based on linear OOA(2730, 132862, F27, 8, 8) (dual of [(132862, 8), 1062866, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2730, 531448, F27, 8) (dual of [531448, 531418, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2730, 531450, F27, 8) (dual of [531450, 531420, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(2729, 531441, F27, 8) (dual of [531441, 531412, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2721, 531441, F27, 6) (dual of [531441, 531420, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(2730, 531450, F27, 8) (dual of [531450, 531420, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2730, 531448, F27, 8) (dual of [531448, 531418, 9]-code), using
- net defined by OOA [i] based on linear OOA(2730, 132862, F27, 8, 8) (dual of [(132862, 8), 1062866, 9]-NRT-code), using
- digital (60, 76, 1048575)-net over F27, using
- net defined by OOA [i] based on linear OOA(2776, 1048575, F27, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2776, 8388600, F27, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2776, 8388600, F27, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(2776, 1048575, F27, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- digital (22, 30, 132862)-net over F27, using
(90, 106, large)-Net over F27 — Digital
Digital (90, 106, large)-net over F27, using
- t-expansion [i] based on digital (84, 106, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(27106, large, F27, 22) (dual of [large, large−106, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(27106, large, F27, 22) (dual of [large, large−106, 23]-code), using
(90, 106, large)-Net in Base 27 — Upper bound on s
There is no (90, 106, large)-net in base 27, because
- 14 times m-reduction [i] would yield (90, 92, large)-net in base 27, but