Best Known (101−29, 101, s)-Nets in Base 27
(101−29, 101, 1474)-Net over F27 — Constructive and digital
Digital (72, 101, 1474)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (53, 82, 1406)-net over F27, using
- net defined by OOA [i] based on linear OOA(2782, 1406, F27, 29, 29) (dual of [(1406, 29), 40692, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2782, 19685, F27, 29) (dual of [19685, 19603, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2782, 19686, F27, 29) (dual of [19686, 19604, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(2782, 19683, F27, 29) (dual of [19683, 19601, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(2782, 19686, F27, 29) (dual of [19686, 19604, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2782, 19685, F27, 29) (dual of [19685, 19603, 30]-code), using
- net defined by OOA [i] based on linear OOA(2782, 1406, F27, 29, 29) (dual of [(1406, 29), 40692, 30]-NRT-code), using
- digital (5, 19, 68)-net over F27, using
(101−29, 101, 1488)-Net in Base 27 — Constructive
(72, 101, 1488)-net in base 27, using
- (u, u+v)-construction [i] based on
- (5, 19, 82)-net in base 27, using
- 1 times m-reduction [i] based on (5, 20, 82)-net in base 27, using
- base change [i] based on digital (0, 15, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- base change [i] based on digital (0, 15, 82)-net over F81, using
- 1 times m-reduction [i] based on (5, 20, 82)-net in base 27, using
- digital (53, 82, 1406)-net over F27, using
- net defined by OOA [i] based on linear OOA(2782, 1406, F27, 29, 29) (dual of [(1406, 29), 40692, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2782, 19685, F27, 29) (dual of [19685, 19603, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2782, 19686, F27, 29) (dual of [19686, 19604, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(2782, 19683, F27, 29) (dual of [19683, 19601, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(2782, 19686, F27, 29) (dual of [19686, 19604, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2782, 19685, F27, 29) (dual of [19685, 19603, 30]-code), using
- net defined by OOA [i] based on linear OOA(2782, 1406, F27, 29, 29) (dual of [(1406, 29), 40692, 30]-NRT-code), using
- (5, 19, 82)-net in base 27, using
(101−29, 101, 63279)-Net over F27 — Digital
Digital (72, 101, 63279)-net over F27, using
(101−29, 101, large)-Net in Base 27 — Upper bound on s
There is no (72, 101, large)-net in base 27, because
- 27 times m-reduction [i] would yield (72, 74, large)-net in base 27, but