Best Known (85−20, 85, s)-Nets in Base 32
(85−20, 85, 104861)-Net over F32 — Constructive and digital
Digital (65, 85, 104861)-net over F32, using
- 321 times duplication [i] based on digital (64, 84, 104861)-net over F32, using
- net defined by OOA [i] based on linear OOA(3284, 104861, F32, 20, 20) (dual of [(104861, 20), 2097136, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3284, 1048610, F32, 20) (dual of [1048610, 1048526, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3284, 1048611, F32, 20) (dual of [1048611, 1048527, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [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(3249, 1048576, F32, 13) (dual of [1048576, 1048527, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(327, 35, F32, 6) (dual of [35, 28, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(327, 43, F32, 6) (dual of [43, 36, 7]-code), using
- algebraic-geometric code AG(F,36P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- discarding factors / shortening the dual code based on linear OA(327, 43, F32, 6) (dual of [43, 36, 7]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3284, 1048611, F32, 20) (dual of [1048611, 1048527, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3284, 1048610, F32, 20) (dual of [1048610, 1048526, 21]-code), using
- net defined by OOA [i] based on linear OOA(3284, 104861, F32, 20, 20) (dual of [(104861, 20), 2097136, 21]-NRT-code), using
(85−20, 85, 209716)-Net in Base 32 — Constructive
(65, 85, 209716)-net in base 32, using
- 321 times duplication [i] based on (64, 84, 209716)-net in base 32, using
- base change [i] based on digital (40, 60, 209716)-net over F128, using
- net defined by OOA [i] based on linear OOA(12860, 209716, F128, 20, 20) (dual of [(209716, 20), 4194260, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(12860, 2097160, F128, 20) (dual of [2097160, 2097100, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12860, 2097163, F128, 20) (dual of [2097163, 2097103, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(12860, 2097163, F128, 20) (dual of [2097163, 2097103, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(12860, 2097160, F128, 20) (dual of [2097160, 2097100, 21]-code), using
- net defined by OOA [i] based on linear OOA(12860, 209716, F128, 20, 20) (dual of [(209716, 20), 4194260, 21]-NRT-code), using
- base change [i] based on digital (40, 60, 209716)-net over F128, using
(85−20, 85, 1384913)-Net over F32 — Digital
Digital (65, 85, 1384913)-net over F32, using
(85−20, 85, large)-Net in Base 32 — Upper bound on s
There is no (65, 85, large)-net in base 32, because
- 18 times m-reduction [i] would yield (65, 67, large)-net in base 32, but