Best Known (27, 27+8, s)-Nets in Base 49
(27, 27+8, 1442377)-Net over F49 — Constructive and digital
Digital (27, 35, 1442377)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 1176)-net over F49, using
- net defined by OOA [i] based on linear OOA(496, 1176, F49, 4, 4) (dual of [(1176, 4), 4698, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(496, 1176, F49, 3, 4) (dual of [(1176, 3), 3522, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- 1 times truncation [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- appending kth column [i] based on linear OOA(496, 1176, F49, 3, 4) (dual of [(1176, 3), 3522, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(496, 1176, F49, 4, 4) (dual of [(1176, 4), 4698, 5]-NRT-code), using
- digital (21, 29, 1441201)-net over F49, using
- net defined by OOA [i] based on linear OOA(4929, 1441201, F49, 8, 8) (dual of [(1441201, 8), 11529579, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(4929, 5764804, F49, 8) (dual of [5764804, 5764775, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4929, 5764805, F49, 8) (dual of [5764805, 5764776, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(4929, 5764805, F49, 8) (dual of [5764805, 5764776, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(4929, 5764804, F49, 8) (dual of [5764804, 5764775, 9]-code), using
- net defined by OOA [i] based on linear OOA(4929, 1441201, F49, 8, 8) (dual of [(1441201, 8), 11529579, 9]-NRT-code), using
- digital (2, 6, 1176)-net over F49, using
(27, 27+8, large)-Net over F49 — Digital
Digital (27, 35, large)-net over F49, using
- 491 times duplication [i] based on digital (26, 34, large)-net over F49, using
(27, 27+8, large)-Net in Base 49 — Upper bound on s
There is no (27, 35, large)-net in base 49, because
- 6 times m-reduction [i] would yield (27, 29, large)-net in base 49, but