Best Known (74, 74+28, s)-Nets in Base 27
(74, 74+28, 1493)-Net over F27 — Constructive and digital
Digital (74, 102, 1493)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 23, 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 (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 (9, 23, 88)-net over F27, using
(74, 74+28, 1522)-Net in Base 27 — Constructive
(74, 102, 1522)-net in base 27, using
- (u, u+v)-construction [i] based on
- (8, 22, 116)-net in base 27, using
- 2 times m-reduction [i] based on (8, 24, 116)-net in base 27, using
- base change [i] based on digital (2, 18, 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, 18, 116)-net over F81, using
- 2 times m-reduction [i] based on (8, 24, 116)-net in base 27, using
- digital (52, 80, 1406)-net over F27, using
- net defined by OOA [i] based on linear OOA(2780, 1406, F27, 28, 28) (dual of [(1406, 28), 39288, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2780, 19684, F27, 28) (dual of [19684, 19604, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2780, 19687, F27, 28) (dual of [19687, 19607, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] 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]
- linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(271, 4, F27, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(2780, 19687, F27, 28) (dual of [19687, 19607, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2780, 19684, F27, 28) (dual of [19684, 19604, 29]-code), using
- net defined by OOA [i] based on linear OOA(2780, 1406, F27, 28, 28) (dual of [(1406, 28), 39288, 29]-NRT-code), using
- (8, 22, 116)-net in base 27, using
(74, 74+28, 107365)-Net over F27 — Digital
Digital (74, 102, 107365)-net over F27, using
(74, 74+28, large)-Net in Base 27 — Upper bound on s
There is no (74, 102, large)-net in base 27, because
- 26 times m-reduction [i] would yield (74, 76, large)-net in base 27, but