Best Known (76, 76+24, s)-Nets in Base 27
(76, 76+24, 44289)-Net over F27 — Constructive and digital
Digital (76, 100, 44289)-net over F27, using
- 272 times duplication [i] based on digital (74, 98, 44289)-net over F27, using
- net defined by OOA [i] based on linear OOA(2798, 44289, F27, 24, 24) (dual of [(44289, 24), 1062838, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2798, 531468, F27, 24) (dual of [531468, 531370, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2798, 531469, F27, 24) (dual of [531469, 531371, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- 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(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(275, 28, F27, 5) (dual of [28, 23, 6]-code or 28-arc in PG(4,27)), using
- extended Reed–Solomon code RSe(23,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(2798, 531469, F27, 24) (dual of [531469, 531371, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2798, 531468, F27, 24) (dual of [531468, 531370, 25]-code), using
- net defined by OOA [i] based on linear OOA(2798, 44289, F27, 24, 24) (dual of [(44289, 24), 1062838, 25]-NRT-code), using
(76, 76+24, 606474)-Net over F27 — Digital
Digital (76, 100, 606474)-net over F27, using
(76, 76+24, large)-Net in Base 27 — Upper bound on s
There is no (76, 100, large)-net in base 27, because
- 22 times m-reduction [i] would yield (76, 78, large)-net in base 27, but