Best Known (75, 75+27, s)-Nets in Base 27
(75, 75+27, 1615)-Net over F27 — Constructive and digital
Digital (75, 102, 1615)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (11, 24, 102)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 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 (4, 17, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (1, 7, 38)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (51, 78, 1513)-net over F27, using
- net defined by OOA [i] based on linear OOA(2778, 1513, F27, 27, 27) (dual of [(1513, 27), 40773, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2778, 19670, F27, 27) (dual of [19670, 19592, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2778, 19682, F27, 27) (dual of [19682, 19604, 28]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2778, 19682, F27, 27) (dual of [19682, 19604, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2778, 19670, F27, 27) (dual of [19670, 19592, 28]-code), using
- net defined by OOA [i] based on linear OOA(2778, 1513, F27, 27, 27) (dual of [(1513, 27), 40773, 28]-NRT-code), using
- digital (11, 24, 102)-net over F27, using
(75, 75+27, 1673)-Net in Base 27 — Constructive
(75, 102, 1673)-net in base 27, using
- (u, u+v)-construction [i] based on
- (11, 24, 160)-net in base 27, using
- base change [i] based on digital (5, 18, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 18, 160)-net over F81, using
- digital (51, 78, 1513)-net over F27, using
- net defined by OOA [i] based on linear OOA(2778, 1513, F27, 27, 27) (dual of [(1513, 27), 40773, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2778, 19670, F27, 27) (dual of [19670, 19592, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2778, 19682, F27, 27) (dual of [19682, 19604, 28]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2778, 19682, F27, 27) (dual of [19682, 19604, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2778, 19670, F27, 27) (dual of [19670, 19592, 28]-code), using
- net defined by OOA [i] based on linear OOA(2778, 1513, F27, 27, 27) (dual of [(1513, 27), 40773, 28]-NRT-code), using
- (11, 24, 160)-net in base 27, using
(75, 75+27, 167380)-Net over F27 — Digital
Digital (75, 102, 167380)-net over F27, using
(75, 75+27, large)-Net in Base 27 — Upper bound on s
There is no (75, 102, large)-net in base 27, because
- 25 times m-reduction [i] would yield (75, 77, large)-net in base 27, but