Best Known (87, 87+22, s)-Nets in Base 27
(87, 87+22, 762600)-Net over F27 — Constructive and digital
Digital (87, 109, 762600)-net over F27, using
- 273 times duplication [i] based on digital (84, 106, 762600)-net over F27, using
- net defined by OOA [i] based on linear OOA(27106, 762600, F27, 22, 22) (dual of [(762600, 22), 16777094, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(27106, 8388600, F27, 22) (dual of [8388600, 8388494, 23]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(27106, large, F27, 22) (dual of [large, large−106, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(27106, 8388600, F27, 22) (dual of [8388600, 8388494, 23]-code), using
- net defined by OOA [i] based on linear OOA(27106, 762600, F27, 22, 22) (dual of [(762600, 22), 16777094, 23]-NRT-code), using
(87, 87+22, large)-Net over F27 — Digital
Digital (87, 109, large)-net over F27, using
- 273 times duplication [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
(87, 87+22, large)-Net in Base 27 — Upper bound on s
There is no (87, 109, large)-net in base 27, because
- 20 times m-reduction [i] would yield (87, 89, large)-net in base 27, but