Best Known (84, 102, s)-Nets in Base 27
(84, 102, 932153)-Net over F27 — Constructive and digital
Digital (84, 102, 932153)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 16, 86)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 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 (2, 11, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (1, 5, 38)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (68, 86, 932067)-net over F27, using
- net defined by OOA [i] based on linear OOA(2786, 932067, F27, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- net defined by OOA [i] based on linear OOA(2786, 932067, F27, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- digital (7, 16, 86)-net over F27, using
(84, 102, 932183)-Net in Base 27 — Constructive
(84, 102, 932183)-net in base 27, using
- 271 times duplication [i] based on (83, 101, 932183)-net in base 27, using
- (u, u+v)-construction [i] based on
- (6, 15, 116)-net in base 27, using
- 1 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- 1 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
- digital (68, 86, 932067)-net over F27, using
- net defined by OOA [i] based on linear OOA(2786, 932067, F27, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- net defined by OOA [i] based on linear OOA(2786, 932067, F27, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- (6, 15, 116)-net in base 27, using
- (u, u+v)-construction [i] based on
(84, 102, large)-Net over F27 — Digital
Digital (84, 102, large)-net over F27, using
- 4 times m-reduction [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
(84, 102, large)-Net in Base 27 — Upper bound on s
There is no (84, 102, large)-net in base 27, because
- 16 times m-reduction [i] would yield (84, 86, large)-net in base 27, but