Best Known (94−25, 94, s)-Nets in Base 27
(94−25, 94, 1728)-Net over F27 — Constructive and digital
Digital (69, 94, 1728)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 21, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (48, 73, 1640)-net over F27, using
- net defined by OOA [i] based on linear OOA(2773, 1640, F27, 25, 25) (dual of [(1640, 25), 40927, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2773, 19681, F27, 25) (dual of [19681, 19608, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2773, 19683, F27, 25) (dual of [19683, 19610, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(2773, 19683, F27, 25) (dual of [19683, 19610, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2773, 19681, F27, 25) (dual of [19681, 19608, 26]-code), using
- net defined by OOA [i] based on linear OOA(2773, 1640, F27, 25, 25) (dual of [(1640, 25), 40927, 26]-NRT-code), using
- digital (9, 21, 88)-net over F27, using
(94−25, 94, 1757)-Net in Base 27 — Constructive
(69, 94, 1757)-net in base 27, using
- (u, u+v)-construction [i] based on
- (7, 19, 116)-net in base 27, using
- 1 times m-reduction [i] based on (7, 20, 116)-net in base 27, using
- base change [i] based on digital (2, 15, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 15, 116)-net over F81, using
- 1 times m-reduction [i] based on (7, 20, 116)-net in base 27, using
- digital (50, 75, 1641)-net over F27, using
- net defined by OOA [i] based on linear OOA(2775, 1641, F27, 25, 25) (dual of [(1641, 25), 40950, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2775, 19693, F27, 25) (dual of [19693, 19618, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2775, 19694, F27, 25) (dual of [19694, 19619, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(2773, 19683, F27, 25) (dual of [19683, 19610, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(272, 11, F27, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2775, 19694, F27, 25) (dual of [19694, 19619, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2775, 19693, F27, 25) (dual of [19693, 19618, 26]-code), using
- net defined by OOA [i] based on linear OOA(2775, 1641, F27, 25, 25) (dual of [(1641, 25), 40950, 26]-NRT-code), using
- (7, 19, 116)-net in base 27, using
(94−25, 94, 152264)-Net over F27 — Digital
Digital (69, 94, 152264)-net over F27, using
(94−25, 94, large)-Net in Base 27 — Upper bound on s
There is no (69, 94, large)-net in base 27, because
- 23 times m-reduction [i] would yield (69, 71, large)-net in base 27, but