Best Known (107−19, 107, s)-Nets in Base 27
(107−19, 107, 932152)-Net over F27 — Constructive and digital
Digital (88, 107, 932152)-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 (72, 91, 932066)-net over F27, using
- net defined by OOA [i] based on linear OOA(2791, 932066, F27, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2791, 8388595, F27, 19) (dual of [8388595, 8388504, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2791, large, F27, 19) (dual of [large, large−91, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2791, large, F27, 19) (dual of [large, large−91, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2791, 8388595, F27, 19) (dual of [8388595, 8388504, 20]-code), using
- net defined by OOA [i] based on linear OOA(2791, 932066, F27, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- digital (7, 16, 86)-net over F27, using
(107−19, 107, 932182)-Net in Base 27 — Constructive
(88, 107, 932182)-net in base 27, using
- 271 times duplication [i] based on (87, 106, 932182)-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 (72, 91, 932066)-net over F27, using
- net defined by OOA [i] based on linear OOA(2791, 932066, F27, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2791, 8388595, F27, 19) (dual of [8388595, 8388504, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2791, large, F27, 19) (dual of [large, large−91, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2791, large, F27, 19) (dual of [large, large−91, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2791, 8388595, F27, 19) (dual of [8388595, 8388504, 20]-code), using
- net defined by OOA [i] based on linear OOA(2791, 932066, F27, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- (6, 15, 116)-net in base 27, using
- (u, u+v)-construction [i] based on
(107−19, 107, large)-Net over F27 — Digital
Digital (88, 107, large)-net over F27, using
- 271 times duplication [i] based on digital (87, 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
(107−19, 107, large)-Net in Base 27 — Upper bound on s
There is no (88, 107, large)-net in base 27, because
- 17 times m-reduction [i] would yield (88, 90, large)-net in base 27, but