Best Known (71, 71+24, s)-Nets in Base 32
(71, 71+24, 87382)-Net over F32 — Constructive and digital
Digital (71, 95, 87382)-net over F32, using
- 321 times duplication [i] based on digital (70, 94, 87382)-net over F32, using
- net defined by OOA [i] based on linear OOA(3294, 87382, F32, 24, 24) (dual of [(87382, 24), 2097074, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3294, 1048584, F32, 24) (dual of [1048584, 1048490, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3294, 1048585, F32, 24) (dual of [1048585, 1048491, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3294, 1048585, F32, 24) (dual of [1048585, 1048491, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3294, 1048584, F32, 24) (dual of [1048584, 1048490, 25]-code), using
- net defined by OOA [i] based on linear OOA(3294, 87382, F32, 24, 24) (dual of [(87382, 24), 2097074, 25]-NRT-code), using
(71, 71+24, 788099)-Net over F32 — Digital
Digital (71, 95, 788099)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3295, 788099, F32, 24) (dual of [788099, 788004, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3295, 1048590, F32, 24) (dual of [1048590, 1048495, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(322, 14, F32, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(3295, 1048590, F32, 24) (dual of [1048590, 1048495, 25]-code), using
(71, 71+24, large)-Net in Base 32 — Upper bound on s
There is no (71, 95, large)-net in base 32, because
- 22 times m-reduction [i] would yield (71, 73, large)-net in base 32, but