Best Known (78, 103, s)-Nets in Base 32
(78, 103, 87384)-Net over F32 — Constructive and digital
Digital (78, 103, 87384)-net over F32, using
- net defined by OOA [i] based on linear OOA(32103, 87384, F32, 25, 25) (dual of [(87384, 25), 2184497, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(32103, 1048609, F32, 25) (dual of [1048609, 1048506, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(24) ⊂ Ce(17) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(32103, 1048609, F32, 25) (dual of [1048609, 1048506, 26]-code), using
(78, 103, 174762)-Net in Base 32 — Constructive
(78, 103, 174762)-net in base 32, using
- net defined by OOA [i] based on OOA(32103, 174762, S32, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32103, 2097145, S32, 25), using
- discarding factors based on OA(32103, 2097155, S32, 25), using
- discarding parts of the base [i] based on linear OA(12873, 2097155, F128, 25) (dual of [2097155, 2097082, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- 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(12870, 2097152, F128, 24) (dual of [2097152, 2097082, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(12873, 2097155, F128, 25) (dual of [2097155, 2097082, 26]-code), using
- discarding factors based on OA(32103, 2097155, S32, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32103, 2097145, S32, 25), using
(78, 103, 1048609)-Net over F32 — Digital
Digital (78, 103, 1048609)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32103, 1048609, F32, 25) (dual of [1048609, 1048506, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(24) ⊂ Ce(17) [i] based on
(78, 103, large)-Net in Base 32 — Upper bound on s
There is no (78, 103, large)-net in base 32, because
- 23 times m-reduction [i] would yield (78, 80, large)-net in base 32, but