Best Known (108−23, 108, s)-Nets in Base 27
(108−23, 108, 48399)-Net over F27 — Constructive and digital
Digital (85, 108, 48399)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 19, 86)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 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 (2, 13, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (1, 6, 38)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (66, 89, 48313)-net over F27, using
- net defined by OOA [i] based on linear OOA(2789, 48313, F27, 23, 23) (dual of [(48313, 23), 1111110, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2789, 531444, F27, 23) (dual of [531444, 531355, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2789, 531445, F27, 23) (dual of [531445, 531356, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(2789, 531441, F27, 23) (dual of [531441, 531352, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2785, 531441, F27, 22) (dual of [531441, 531356, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 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(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2789, 531445, F27, 23) (dual of [531445, 531356, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2789, 531444, F27, 23) (dual of [531444, 531355, 24]-code), using
- net defined by OOA [i] based on linear OOA(2789, 48313, F27, 23, 23) (dual of [(48313, 23), 1111110, 24]-NRT-code), using
- digital (8, 19, 86)-net over F27, using
(108−23, 108, 48429)-Net in Base 27 — Constructive
(85, 108, 48429)-net in base 27, using
- base change [i] based on digital (58, 81, 48429)-net over F81, using
- 811 times duplication [i] based on digital (57, 80, 48429)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 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
- digital (44, 67, 48313)-net over F81, using
- net defined by OOA [i] based on linear OOA(8167, 48313, F81, 23, 23) (dual of [(48313, 23), 1111132, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8167, 531444, F81, 23) (dual of [531444, 531377, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(8167, 531441, F81, 23) (dual of [531441, 531374, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8164, 531441, F81, 22) (dual of [531441, 531377, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- OOA 11-folding and stacking with additional row [i] based on linear OA(8167, 531444, F81, 23) (dual of [531444, 531377, 24]-code), using
- net defined by OOA [i] based on linear OOA(8167, 48313, F81, 23, 23) (dual of [(48313, 23), 1111132, 24]-NRT-code), using
- digital (2, 13, 116)-net over F81, using
- (u, u+v)-construction [i] based on
- 811 times duplication [i] based on digital (57, 80, 48429)-net over F81, using
(108−23, 108, 3703188)-Net over F27 — Digital
Digital (85, 108, 3703188)-net over F27, using
(108−23, 108, large)-Net in Base 27 — Upper bound on s
There is no (85, 108, large)-net in base 27, because
- 21 times m-reduction [i] would yield (85, 87, large)-net in base 27, but