Best Known (79−25, 79, s)-Nets in Base 32
(79−25, 79, 2732)-Net over F32 — Constructive and digital
Digital (54, 79, 2732)-net over F32, using
- 322 times duplication [i] based on digital (52, 77, 2732)-net over F32, using
- net defined by OOA [i] based on linear OOA(3277, 2732, F32, 25, 25) (dual of [(2732, 25), 68223, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3277, 32785, F32, 25) (dual of [32785, 32708, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3277, 32787, F32, 25) (dual of [32787, 32710, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3273, 32768, F32, 25) (dual of [32768, 32695, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(324, 19, F32, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3277, 32787, F32, 25) (dual of [32787, 32710, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3277, 32785, F32, 25) (dual of [32785, 32708, 26]-code), using
- net defined by OOA [i] based on linear OOA(3277, 2732, F32, 25, 25) (dual of [(2732, 25), 68223, 26]-NRT-code), using
(79−25, 79, 5461)-Net in Base 32 — Constructive
(54, 79, 5461)-net in base 32, using
- net defined by OOA [i] based on OOA(3279, 5461, S32, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(3279, 65533, S32, 25), using
- discarding factors based on OA(3279, 65538, S32, 25), using
- discarding parts of the base [i] based on linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- discarding factors based on OA(3279, 65538, S32, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(3279, 65533, S32, 25), using
(79−25, 79, 32795)-Net over F32 — Digital
Digital (54, 79, 32795)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3279, 32795, F32, 25) (dual of [32795, 32716, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(3273, 32768, F32, 25) (dual of [32768, 32695, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3252, 32768, F32, 18) (dual of [32768, 32716, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(326, 27, F32, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
(79−25, 79, large)-Net in Base 32 — Upper bound on s
There is no (54, 79, large)-net in base 32, because
- 23 times m-reduction [i] would yield (54, 56, large)-net in base 32, but