Best Known (84−22, 84, s)-Nets in Base 27
(84−22, 84, 1885)-Net over F27 — Constructive and digital
Digital (62, 84, 1885)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 20, 96)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- digital (2, 13, 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 (2, 7, 351)-net over F27, using
- (u, u+v)-construction [i] based on
- 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 (9, 20, 96)-net over F27, using
(84−22, 84, 1939)-Net in Base 27 — Constructive
(62, 84, 1939)-net in base 27, using
- (u, u+v)-construction [i] based on
- (9, 20, 150)-net in base 27, using
- base change [i] based on digital (4, 15, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- base change [i] based on digital (4, 15, 150)-net over F81, 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
- (9, 20, 150)-net in base 27, using
(84−22, 84, 177419)-Net over F27 — Digital
Digital (62, 84, 177419)-net over F27, using
(84−22, 84, large)-Net in Base 27 — Upper bound on s
There is no (62, 84, large)-net in base 27, because
- 20 times m-reduction [i] would yield (62, 64, large)-net in base 27, but