Best Known (53, 53+20, s)-Nets in Base 27
(53, 53+20, 2036)-Net over F27 — Constructive and digital
Digital (53, 73, 2036)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (38, 58, 1968)-net over F27, using
- net defined by OOA [i] based on linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2758, 19680, F27, 20) (dual of [19680, 19622, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2758, 19680, F27, 20) (dual of [19680, 19622, 21]-code), using
- net defined by OOA [i] based on linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code), using
- digital (5, 15, 68)-net over F27, using
(53, 53+20, 2068)-Net in Base 27 — Constructive
(53, 73, 2068)-net in base 27, using
- (u, u+v)-construction [i] based on
- (5, 15, 100)-net in base 27, using
- 1 times m-reduction [i] based on (5, 16, 100)-net in base 27, using
- base change [i] based on digital (1, 12, 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, 12, 100)-net over F81, using
- 1 times m-reduction [i] based on (5, 16, 100)-net in base 27, using
- digital (38, 58, 1968)-net over F27, using
- net defined by OOA [i] based on linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2758, 19680, F27, 20) (dual of [19680, 19622, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2758, 19680, F27, 20) (dual of [19680, 19622, 21]-code), using
- net defined by OOA [i] based on linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code), using
- (5, 15, 100)-net in base 27, using
(53, 53+20, 96324)-Net over F27 — Digital
Digital (53, 73, 96324)-net over F27, using
(53, 53+20, large)-Net in Base 27 — Upper bound on s
There is no (53, 73, large)-net in base 27, because
- 18 times m-reduction [i] would yield (53, 55, large)-net in base 27, but