Best Known (79, 79+21, s)-Nets in Base 27
(79, 79+21, 53290)-Net over F27 — Constructive and digital
Digital (79, 100, 53290)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 19, 146)-net over F27, using
- net defined by OOA [i] based on linear OOA(2719, 146, F27, 10, 10) (dual of [(146, 10), 1441, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2719, 730, F27, 10) (dual of [730, 711, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2719, 731, F27, 10) (dual of [731, 712, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(2719, 729, F27, 10) (dual of [729, 710, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2717, 729, F27, 9) (dual of [729, 712, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 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(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(2719, 731, F27, 10) (dual of [731, 712, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2719, 730, F27, 10) (dual of [730, 711, 11]-code), using
- net defined by OOA [i] based on linear OOA(2719, 146, F27, 10, 10) (dual of [(146, 10), 1441, 11]-NRT-code), using
- digital (60, 81, 53144)-net over F27, using
- net defined by OOA [i] based on linear OOA(2781, 53144, F27, 21, 21) (dual of [(53144, 21), 1115943, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 10-folding and stacking with additional row [i] based on linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using
- net defined by OOA [i] based on linear OOA(2781, 53144, F27, 21, 21) (dual of [(53144, 21), 1115943, 22]-NRT-code), using
- digital (9, 19, 146)-net over F27, using
(79, 79+21, 53294)-Net in Base 27 — Constructive
(79, 100, 53294)-net in base 27, using
- base change [i] based on digital (54, 75, 53294)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- digital (40, 61, 53144)-net over F81, using
- net defined by OOA [i] based on linear OOA(8161, 53144, F81, 21, 21) (dual of [(53144, 21), 1115963, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 10-folding and stacking with additional row [i] based on linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using
- net defined by OOA [i] based on linear OOA(8161, 53144, F81, 21, 21) (dual of [(53144, 21), 1115963, 22]-NRT-code), using
- digital (4, 14, 150)-net over F81, using
- (u, u+v)-construction [i] based on
(79, 79+21, 4583029)-Net over F27 — Digital
Digital (79, 100, 4583029)-net over F27, using
(79, 79+21, large)-Net in Base 27 — Upper bound on s
There is no (79, 100, large)-net in base 27, because
- 19 times m-reduction [i] would yield (79, 81, large)-net in base 27, but