Best Known (68, 68+28, s)-Nets in Base 27
(68, 68+28, 1457)-Net over F27 — Constructive and digital
Digital (68, 96, 1457)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (51, 79, 1405)-net over F27, using
- net defined by OOA [i] based on linear OOA(2779, 1405, F27, 28, 28) (dual of [(1405, 28), 39261, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2779, 19670, F27, 28) (dual of [19670, 19591, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2779, 19670, F27, 28) (dual of [19670, 19591, 29]-code), using
- net defined by OOA [i] based on linear OOA(2779, 1405, F27, 28, 28) (dual of [(1405, 28), 39261, 29]-NRT-code), using
- digital (3, 17, 52)-net over F27, using
(68, 68+28, 51623)-Net over F27 — Digital
Digital (68, 96, 51623)-net over F27, using
(68, 68+28, large)-Net in Base 27 — Upper bound on s
There is no (68, 96, large)-net in base 27, because
- 26 times m-reduction [i] would yield (68, 70, large)-net in base 27, but