Best Known (76, 76+32, s)-Nets in Base 27
(76, 76+32, 1268)-Net over F27 — Constructive and digital
Digital (76, 108, 1268)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 17, 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 (59, 91, 1230)-net over F27, using
- net defined by OOA [i] based on linear OOA(2791, 1230, F27, 32, 32) (dual of [(1230, 32), 39269, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(2791, 19680, F27, 32) (dual of [19680, 19589, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2791, 19683, F27, 32) (dual of [19683, 19592, 33]-code), using
- an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- discarding factors / shortening the dual code based on linear OA(2791, 19683, F27, 32) (dual of [19683, 19592, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(2791, 19680, F27, 32) (dual of [19680, 19589, 33]-code), using
- net defined by OOA [i] based on linear OOA(2791, 1230, F27, 32, 32) (dual of [(1230, 32), 39269, 33]-NRT-code), using
- digital (1, 17, 38)-net over F27, using
(76, 76+32, 46333)-Net over F27 — Digital
Digital (76, 108, 46333)-net over F27, using
(76, 76+32, large)-Net in Base 27 — Upper bound on s
There is no (76, 108, large)-net in base 27, because
- 30 times m-reduction [i] would yield (76, 78, large)-net in base 27, but