Best Known (79, 79+24, s)-Nets in Base 27
(79, 79+24, 44290)-Net over F27 — Constructive and digital
Digital (79, 103, 44290)-net over F27, using
- 271 times duplication [i] based on digital (78, 102, 44290)-net over F27, using
- net defined by OOA [i] based on linear OOA(27102, 44290, F27, 24, 24) (dual of [(44290, 24), 1062858, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(27102, 531480, F27, 24) (dual of [531480, 531378, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(27102, 531482, F27, 24) (dual of [531482, 531380, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- linear OA(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(279, 41, F27, 7) (dual of [41, 32, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(279, 48, F27, 7) (dual of [48, 39, 8]-code), using
- extended algebraic-geometric code AGe(F,40P) [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- discarding factors / shortening the dual code based on linear OA(279, 48, F27, 7) (dual of [48, 39, 8]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(27102, 531482, F27, 24) (dual of [531482, 531380, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(27102, 531480, F27, 24) (dual of [531480, 531378, 25]-code), using
- net defined by OOA [i] based on linear OOA(27102, 44290, F27, 24, 24) (dual of [(44290, 24), 1062858, 25]-NRT-code), using
(79, 79+24, 932199)-Net over F27 — Digital
Digital (79, 103, 932199)-net over F27, using
(79, 79+24, large)-Net in Base 27 — Upper bound on s
There is no (79, 103, large)-net in base 27, because
- 22 times m-reduction [i] would yield (79, 81, large)-net in base 27, but