Best Known (100−25, 100, s)-Nets in Base 32
(100−25, 100, 87382)-Net over F32 — Constructive and digital
Digital (75, 100, 87382)-net over F32, using
- 322 times duplication [i] based on digital (73, 98, 87382)-net over F32, using
- net defined by OOA [i] based on linear OOA(3298, 87382, F32, 25, 25) (dual of [(87382, 25), 2184452, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3298, 1048585, F32, 25) (dual of [1048585, 1048487, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3298, 1048586, F32, 25) (dual of [1048586, 1048488, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- linear OA(3297, 1048577, F32, 25) (dual of [1048577, 1048480, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3289, 1048577, F32, 23) (dual of [1048577, 1048488, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [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 C([0,12]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3298, 1048586, F32, 25) (dual of [1048586, 1048488, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3298, 1048585, F32, 25) (dual of [1048585, 1048487, 26]-code), using
- net defined by OOA [i] based on linear OOA(3298, 87382, F32, 25, 25) (dual of [(87382, 25), 2184452, 26]-NRT-code), using
(100−25, 100, 915753)-Net over F32 — Digital
Digital (75, 100, 915753)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32100, 915753, F32, 25) (dual of [915753, 915653, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(32100, 1048596, F32, 25) (dual of [1048596, 1048496, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(3297, 1048577, F32, 25) (dual of [1048577, 1048480, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3281, 1048577, F32, 21) (dual of [1048577, 1048496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(323, 19, F32, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(32100, 1048596, F32, 25) (dual of [1048596, 1048496, 26]-code), using
(100−25, 100, large)-Net in Base 32 — Upper bound on s
There is no (75, 100, large)-net in base 32, because
- 23 times m-reduction [i] would yield (75, 77, large)-net in base 32, but