Best Known (60, 60+22, s)-Nets in Base 27
(60, 60+22, 1871)-Net over F27 — Constructive and digital
Digital (60, 82, 1871)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 18, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (42, 64, 1789)-net over F27, using
- net defined by OOA [i] based on linear OOA(2764, 1789, F27, 22, 22) (dual of [(1789, 22), 39294, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2764, 19679, F27, 22) (dual of [19679, 19615, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2764, 19679, F27, 22) (dual of [19679, 19615, 23]-code), using
- net defined by OOA [i] based on linear OOA(2764, 1789, F27, 22, 22) (dual of [(1789, 22), 39294, 23]-NRT-code), using
- digital (7, 18, 82)-net over F27, using
(60, 60+22, 1905)-Net in Base 27 — Constructive
(60, 82, 1905)-net in base 27, using
- (u, u+v)-construction [i] based on
- (7, 18, 116)-net in base 27, using
- 2 times m-reduction [i] based on (7, 20, 116)-net in base 27, using
- base change [i] based on digital (2, 15, 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, 15, 116)-net over F81, using
- 2 times m-reduction [i] based on (7, 20, 116)-net in base 27, using
- digital (42, 64, 1789)-net over F27, using
- net defined by OOA [i] based on linear OOA(2764, 1789, F27, 22, 22) (dual of [(1789, 22), 39294, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2764, 19679, F27, 22) (dual of [19679, 19615, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2764, 19679, F27, 22) (dual of [19679, 19615, 23]-code), using
- net defined by OOA [i] based on linear OOA(2764, 1789, F27, 22, 22) (dual of [(1789, 22), 39294, 23]-NRT-code), using
- (7, 18, 116)-net in base 27, using
(60, 60+22, 129625)-Net over F27 — Digital
Digital (60, 82, 129625)-net over F27, using
(60, 60+22, large)-Net in Base 27 — Upper bound on s
There is no (60, 82, large)-net in base 27, because
- 20 times m-reduction [i] would yield (60, 62, large)-net in base 27, but