Best Known (87, 87+20, s)-Nets in Base 27
(87, 87+20, 838898)-Net over F27 — Constructive and digital
Digital (87, 107, 838898)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (76, 96, 838860)-net over F27, using
- net defined by OOA [i] based on linear OOA(2796, 838860, F27, 20, 20) (dual of [(838860, 20), 16777104, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2796, 8388600, F27, 20) (dual of [8388600, 8388504, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2796, large, F27, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2796, large, F27, 20) (dual of [large, large−96, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2796, 8388600, F27, 20) (dual of [8388600, 8388504, 21]-code), using
- net defined by OOA [i] based on linear OOA(2796, 838860, F27, 20, 20) (dual of [(838860, 20), 16777104, 21]-NRT-code), using
- digital (1, 11, 38)-net over F27, using
(87, 87+20, large)-Net over F27 — Digital
Digital (87, 107, large)-net over F27, using
- 271 times duplication [i] based on digital (86, 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
(87, 87+20, large)-Net in Base 27 — Upper bound on s
There is no (87, 107, large)-net in base 27, because
- 18 times m-reduction [i] would yield (87, 89, large)-net in base 27, but