Best Known (110−37, 110, s)-Nets in Base 32
(110−37, 110, 1821)-Net over F32 — Constructive and digital
Digital (73, 110, 1821)-net over F32, using
- 322 times duplication [i] based on digital (71, 108, 1821)-net over F32, using
- net defined by OOA [i] based on linear OOA(32108, 1821, F32, 37, 37) (dual of [(1821, 37), 67269, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(32108, 32779, F32, 37) (dual of [32779, 32671, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(33) [i] based on
- linear OA(32106, 32768, F32, 37) (dual of [32768, 32662, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3297, 32768, F32, 34) (dual of [32768, 32671, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(322, 11, F32, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(36) ⊂ Ce(33) [i] based on
- OOA 18-folding and stacking with additional row [i] based on linear OA(32108, 32779, F32, 37) (dual of [32779, 32671, 38]-code), using
- net defined by OOA [i] based on linear OOA(32108, 1821, F32, 37, 37) (dual of [(1821, 37), 67269, 38]-NRT-code), using
(110−37, 110, 21828)-Net over F32 — Digital
Digital (73, 110, 21828)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32110, 21828, F32, 37) (dual of [21828, 21718, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(32110, 32776, F32, 37) (dual of [32776, 32666, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,17]) [i] based on
- linear OA(32109, 32769, F32, 37) (dual of [32769, 32660, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(32103, 32769, F32, 35) (dual of [32769, 32666, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 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([0,18]) ⊂ C([0,17]) [i] based on
- discarding factors / shortening the dual code based on linear OA(32110, 32776, F32, 37) (dual of [32776, 32666, 38]-code), using
(110−37, 110, large)-Net in Base 32 — Upper bound on s
There is no (73, 110, large)-net in base 32, because
- 35 times m-reduction [i] would yield (73, 75, large)-net in base 32, but