Best Known (109−30, 109, s)-Nets in Base 27
(109−30, 109, 1400)-Net over F27 — Constructive and digital
Digital (79, 109, 1400)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 24, 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 (55, 85, 1312)-net over F27, using
- net defined by OOA [i] based on linear OOA(2785, 1312, F27, 30, 30) (dual of [(1312, 30), 39275, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(2785, 19680, F27, 30) (dual of [19680, 19595, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(2785, 19680, F27, 30) (dual of [19680, 19595, 31]-code), using
- net defined by OOA [i] based on linear OOA(2785, 1312, F27, 30, 30) (dual of [(1312, 30), 39275, 31]-NRT-code), using
- digital (9, 24, 88)-net over F27, using
(109−30, 109, 1428)-Net in Base 27 — Constructive
(79, 109, 1428)-net in base 27, using
- 271 times duplication [i] based on (78, 108, 1428)-net in base 27, using
- (u, u+v)-construction [i] based on
- (8, 23, 116)-net in base 27, using
- 1 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
- 1 times m-reduction [i] based on (8, 24, 116)-net in base 27, using
- digital (55, 85, 1312)-net over F27, using
- net defined by OOA [i] based on linear OOA(2785, 1312, F27, 30, 30) (dual of [(1312, 30), 39275, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(2785, 19680, F27, 30) (dual of [19680, 19595, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(2785, 19680, F27, 30) (dual of [19680, 19595, 31]-code), using
- net defined by OOA [i] based on linear OOA(2785, 1312, F27, 30, 30) (dual of [(1312, 30), 39275, 31]-NRT-code), using
- (8, 23, 116)-net in base 27, using
- (u, u+v)-construction [i] based on
(109−30, 109, 107686)-Net over F27 — Digital
Digital (79, 109, 107686)-net over F27, using
(109−30, 109, large)-Net in Base 27 — Upper bound on s
There is no (79, 109, large)-net in base 27, because
- 28 times m-reduction [i] would yield (79, 81, large)-net in base 27, but