Best Known (79, 110, s)-Nets in Base 32
(79, 110, 2249)-Net over F32 — Constructive and digital
Digital (79, 110, 2249)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (61, 92, 2185)-net over F32, using
- net defined by OOA [i] based on linear OOA(3292, 2185, F32, 31, 31) (dual of [(2185, 31), 67643, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(3292, 32776, F32, 31) (dual of [32776, 32684, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
- linear OA(3291, 32769, F32, 31) (dual of [32769, 32678, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3285, 32769, F32, 29) (dual of [32769, 32684, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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([0,15]) ⊂ C([0,14]) [i] based on
- OOA 15-folding and stacking with additional row [i] based on linear OA(3292, 32776, F32, 31) (dual of [32776, 32684, 32]-code), using
- net defined by OOA [i] based on linear OOA(3292, 2185, F32, 31, 31) (dual of [(2185, 31), 67643, 32]-NRT-code), using
- digital (3, 18, 64)-net over F32, using
(79, 110, 17476)-Net in Base 32 — Constructive
(79, 110, 17476)-net in base 32, using
- net defined by OOA [i] based on OOA(32110, 17476, S32, 31, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(32110, 262141, S32, 31), using
- discarding factors based on OA(32110, 262147, S32, 31), using
- discarding parts of the base [i] based on linear OA(6491, 262147, F64, 31) (dual of [262147, 262056, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- linear OA(6491, 262144, F64, 31) (dual of [262144, 262053, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(6488, 262144, F64, 30) (dual of [262144, 262056, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- discarding parts of the base [i] based on linear OA(6491, 262147, F64, 31) (dual of [262147, 262056, 32]-code), using
- discarding factors based on OA(32110, 262147, S32, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(32110, 262141, S32, 31), using
(79, 110, 128340)-Net over F32 — Digital
Digital (79, 110, 128340)-net over F32, using
(79, 110, large)-Net in Base 32 — Upper bound on s
There is no (79, 110, large)-net in base 32, because
- 29 times m-reduction [i] would yield (79, 81, large)-net in base 32, but