Best Known (47, 55, s)-Nets in Base 4
(47, 55, 65538)-Net over F4 — Constructive and digital
Digital (47, 55, 65538)-net over F4, using
- net defined by OOA [i] based on linear OOA(455, 65538, F4, 8, 8) (dual of [(65538, 8), 524249, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(455, 262152, F4, 8) (dual of [262152, 262097, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(455, 262154, F4, 8) (dual of [262154, 262099, 9]-code), using
- 1 times truncation [i] based on linear OA(456, 262155, F4, 9) (dual of [262155, 262099, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(446, 262144, F4, 7) (dual of [262144, 262098, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
- dual of repetition code with length 11 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(456, 262155, F4, 9) (dual of [262155, 262099, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(455, 262154, F4, 8) (dual of [262154, 262099, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(455, 262152, F4, 8) (dual of [262152, 262097, 9]-code), using
(47, 55, 261598)-Net over F4 — Digital
Digital (47, 55, 261598)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(455, 261598, F4, 8) (dual of [261598, 261543, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(455, 262154, F4, 8) (dual of [262154, 262099, 9]-code), using
- 1 times truncation [i] based on linear OA(456, 262155, F4, 9) (dual of [262155, 262099, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(446, 262144, F4, 7) (dual of [262144, 262098, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
- dual of repetition code with length 11 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(456, 262155, F4, 9) (dual of [262155, 262099, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(455, 262154, F4, 8) (dual of [262154, 262099, 9]-code), using
(47, 55, large)-Net in Base 4 — Upper bound on s
There is no (47, 55, large)-net in base 4, because
- 6 times m-reduction [i] would yield (47, 49, large)-net in base 4, but