Best Known (91, 91+16, s)-Nets in Base 27
(91, 91+16, 1181438)-Net over F27 — Constructive and digital
Digital (91, 107, 1181438)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (23, 31, 132863)-net over F27, using
- net defined by OOA [i] based on linear OOA(2731, 132863, F27, 8, 8) (dual of [(132863, 8), 1062873, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2731, 531452, F27, 8) (dual of [531452, 531421, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2731, 531455, F27, 8) (dual of [531455, 531424, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [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(2717, 531441, F27, 5) (dual of [531441, 531424, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(272, 14, F27, 2) (dual of [14, 12, 3]-code or 14-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(7) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(2731, 531455, F27, 8) (dual of [531455, 531424, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2731, 531452, F27, 8) (dual of [531452, 531421, 9]-code), using
- net defined by OOA [i] based on linear OOA(2731, 132863, F27, 8, 8) (dual of [(132863, 8), 1062873, 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 (23, 31, 132863)-net over F27, using
(91, 91+16, large)-Net over F27 — Digital
Digital (91, 107, large)-net over F27, using
- 271 times duplication [i] based on 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
- t-expansion [i] based on digital (84, 106, large)-net over F27, using
(91, 91+16, large)-Net in Base 27 — Upper bound on s
There is no (91, 107, large)-net in base 27, because
- 14 times m-reduction [i] would yield (91, 93, large)-net in base 27, but