Best Known (108−26, 108, s)-Nets in Base 32
(108−26, 108, 80662)-Net over F32 — Constructive and digital
Digital (82, 108, 80662)-net over F32, using
- 321 times duplication [i] based on digital (81, 107, 80662)-net over F32, using
- net defined by OOA [i] based on linear OOA(32107, 80662, F32, 26, 26) (dual of [(80662, 26), 2097105, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(32107, 1048606, F32, 26) (dual of [1048606, 1048499, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(32107, 1048609, F32, 26) (dual of [1048609, 1048502, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(32101, 1048576, F32, 26) (dual of [1048576, 1048475, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(326, 33, F32, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
- extended Reed–Solomon code RSe(27,32) [i]
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(32107, 1048609, F32, 26) (dual of [1048609, 1048502, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(32107, 1048606, F32, 26) (dual of [1048606, 1048499, 27]-code), using
- net defined by OOA [i] based on linear OOA(32107, 80662, F32, 26, 26) (dual of [(80662, 26), 2097105, 27]-NRT-code), using
(108−26, 108, 161319)-Net in Base 32 — Constructive
(82, 108, 161319)-net in base 32, using
- 321 times duplication [i] based on (81, 107, 161319)-net in base 32, using
- net defined by OOA [i] based on OOA(32107, 161319, S32, 26, 26), using
- OA 13-folding and stacking [i] based on OA(32107, 2097147, S32, 26), using
- discarding factors based on OA(32107, 2097155, S32, 26), using
- discarding parts of the base [i] based on linear OA(12876, 2097155, F128, 26) (dual of [2097155, 2097079, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(12876, 2097152, F128, 26) (dual of [2097152, 2097076, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- discarding parts of the base [i] based on linear OA(12876, 2097155, F128, 26) (dual of [2097155, 2097079, 27]-code), using
- discarding factors based on OA(32107, 2097155, S32, 26), using
- OA 13-folding and stacking [i] based on OA(32107, 2097147, S32, 26), using
- net defined by OOA [i] based on OOA(32107, 161319, S32, 26, 26), using
(108−26, 108, 1048611)-Net over F32 — Digital
Digital (82, 108, 1048611)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32108, 1048611, F32, 26) (dual of [1048611, 1048503, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(32101, 1048576, F32, 26) (dual of [1048576, 1048475, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(25) ⊂ Ce(18) [i] based on
(108−26, 108, large)-Net in Base 32 — Upper bound on s
There is no (82, 108, large)-net in base 32, because
- 24 times m-reduction [i] would yield (82, 84, large)-net in base 32, but