Best Known (81−20, 81, s)-Nets in Base 32
(81−20, 81, 104860)-Net over F32 — Constructive and digital
Digital (61, 81, 104860)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 104860, F32, 20, 20) (dual of [(104860, 20), 2097119, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3281, 1048600, F32, 20) (dual of [1048600, 1048519, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-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(19) ⊂ Ce(14) [i] based on
- OA 10-folding and stacking [i] based on linear OA(3281, 1048600, F32, 20) (dual of [1048600, 1048519, 21]-code), using
(81−20, 81, 1048600)-Net over F32 — Digital
Digital (61, 81, 1048600)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3281, 1048600, F32, 20) (dual of [1048600, 1048519, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-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(19) ⊂ Ce(14) [i] based on
(81−20, 81, large)-Net in Base 32 — Upper bound on s
There is no (61, 81, large)-net in base 32, because
- 18 times m-reduction [i] would yield (61, 63, large)-net in base 32, but