Best Known (21, 21+7, s)-Nets in Base 27
(21, 21+7, 177176)-Net over F27 — Constructive and digital
Digital (21, 28, 177176)-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 (18, 25, 177148)-net over F27, using
- net defined by OOA [i] based on linear OOA(2725, 177148, F27, 7, 7) (dual of [(177148, 7), 1240011, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2725, 531445, F27, 7) (dual of [531445, 531420, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(2725, 531441, F27, 7) (dual of [531441, 531416, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2721, 531441, F27, 6) (dual of [531441, 531420, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(2725, 531445, F27, 7) (dual of [531445, 531420, 8]-code), using
- net defined by OOA [i] based on linear OOA(2725, 177148, F27, 7, 7) (dual of [(177148, 7), 1240011, 8]-NRT-code), using
- digital (0, 3, 28)-net over F27, using
(21, 21+7, 550743)-Net over F27 — Digital
Digital (21, 28, 550743)-net over F27, using
(21, 21+7, large)-Net in Base 27 — Upper bound on s
There is no (21, 28, large)-net in base 27, because
- 5 times m-reduction [i] would yield (21, 23, large)-net in base 27, but