Best Known (82, 106, s)-Nets in Base 27
(82, 106, 44325)-Net over F27 — Constructive and digital
Digital (82, 106, 44325)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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 (69, 93, 44287)-net over F27, using
- net defined by OOA [i] based on linear OOA(2793, 44287, F27, 24, 24) (dual of [(44287, 24), 1062795, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2793, 531444, F27, 24) (dual of [531444, 531351, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2793, 531445, F27, 24) (dual of [531445, 531352, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2789, 531441, F27, 23) (dual of [531441, 531352, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2793, 531445, F27, 24) (dual of [531445, 531352, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2793, 531444, F27, 24) (dual of [531444, 531351, 25]-code), using
- net defined by OOA [i] based on linear OOA(2793, 44287, F27, 24, 24) (dual of [(44287, 24), 1062795, 25]-NRT-code), using
- digital (1, 13, 38)-net over F27, using
(82, 106, 1432869)-Net over F27 — Digital
Digital (82, 106, 1432869)-net over F27, using
(82, 106, large)-Net in Base 27 — Upper bound on s
There is no (82, 106, large)-net in base 27, because
- 22 times m-reduction [i] would yield (82, 84, large)-net in base 27, but