Best Known (72, 104, s)-Nets in Base 27
(72, 104, 1233)-Net over F27 — Constructive and digital
Digital (72, 104, 1233)-net over F27, using
- net defined by OOA [i] based on linear OOA(27104, 1233, F27, 32, 32) (dual of [(1233, 32), 39352, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(27104, 19728, F27, 32) (dual of [19728, 19624, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(27104, 19729, F27, 32) (dual of [19729, 19625, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(19) [i] based on
- linear OA(2791, 19683, F27, 32) (dual of [19683, 19592, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2713, 46, F27, 11) (dual of [46, 33, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2713, 48, F27, 11) (dual of [48, 35, 12]-code), using
- extended algebraic-geometric code AGe(F,36P) [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(2713, 48, F27, 11) (dual of [48, 35, 12]-code), using
- construction X applied to Ce(31) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(27104, 19729, F27, 32) (dual of [19729, 19625, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(27104, 19728, F27, 32) (dual of [19728, 19624, 33]-code), using
(72, 104, 30288)-Net over F27 — Digital
Digital (72, 104, 30288)-net over F27, using
(72, 104, large)-Net in Base 27 — Upper bound on s
There is no (72, 104, large)-net in base 27, because
- 30 times m-reduction [i] would yield (72, 74, large)-net in base 27, but