Best Known (21, 30, s)-Nets in Base 27
(21, 30, 4959)-Net over F27 — Constructive and digital
Digital (21, 30, 4959)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 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 (16, 25, 4921)-net over F27, using
- net defined by OOA [i] based on linear OOA(2725, 4921, F27, 9, 9) (dual of [(4921, 9), 44264, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2725, 19685, F27, 9) (dual of [19685, 19660, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2725, 19686, F27, 9) (dual of [19686, 19661, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(2725, 19683, F27, 9) (dual of [19683, 19658, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2722, 19683, F27, 8) (dual of [19683, 19661, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 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(8) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(2725, 19686, F27, 9) (dual of [19686, 19661, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2725, 19685, F27, 9) (dual of [19685, 19660, 10]-code), using
- net defined by OOA [i] based on linear OOA(2725, 4921, F27, 9, 9) (dual of [(4921, 9), 44264, 10]-NRT-code), using
- digital (1, 5, 38)-net over F27, using
(21, 30, 33758)-Net over F27 — Digital
Digital (21, 30, 33758)-net over F27, using
(21, 30, large)-Net in Base 27 — Upper bound on s
There is no (21, 30, large)-net in base 27, because
- 7 times m-reduction [i] would yield (21, 23, large)-net in base 27, but