Best Known (63, 63+14, s)-Nets in Base 27
(63, 63+14, 1198437)-Net over F27 — Constructive and digital
Digital (63, 77, 1198437)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 11, 66)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (1, 8, 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 (0, 3, 28)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (52, 66, 1198371)-net over F27, using
- net defined by OOA [i] based on linear OOA(2766, 1198371, F27, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2766, 8388597, F27, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2766, large, F27, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2766, large, F27, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2766, 8388597, F27, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(2766, 1198371, F27, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- digital (4, 11, 66)-net over F27, using
(63, 63+14, 1198471)-Net in Base 27 — Constructive
(63, 77, 1198471)-net in base 27, using
- (u, u+v)-construction [i] based on
- (4, 11, 100)-net in base 27, using
- 1 times m-reduction [i] based on (4, 12, 100)-net in base 27, using
- base change [i] based on digital (1, 9, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 9, 100)-net over F81, using
- 1 times m-reduction [i] based on (4, 12, 100)-net in base 27, using
- digital (52, 66, 1198371)-net over F27, using
- net defined by OOA [i] based on linear OOA(2766, 1198371, F27, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2766, 8388597, F27, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2766, large, F27, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2766, large, F27, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2766, 8388597, F27, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(2766, 1198371, F27, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- (4, 11, 100)-net in base 27, using
(63, 63+14, large)-Net over F27 — Digital
Digital (63, 77, large)-net over F27, using
- 271 times duplication [i] based on digital (62, 76, large)-net over F27, using
- t-expansion [i] based on digital (60, 76, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- t-expansion [i] based on digital (60, 76, large)-net over F27, using
(63, 63+14, large)-Net in Base 27 — Upper bound on s
There is no (63, 77, large)-net in base 27, because
- 12 times m-reduction [i] would yield (63, 65, large)-net in base 27, but