Best Known (28−14, 28, s)-Nets in Base 32
(28−14, 28, 147)-Net over F32 — Constructive and digital
Digital (14, 28, 147)-net over F32, using
- net defined by OOA [i] based on linear OOA(3228, 147, F32, 14, 14) (dual of [(147, 14), 2030, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3228, 1029, F32, 14) (dual of [1029, 1001, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(3227, 1024, F32, 14) (dual of [1024, 997, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3223, 1024, F32, 12) (dual of [1024, 1001, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 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 Ce(13) ⊂ Ce(11) [i] based on
- OA 7-folding and stacking [i] based on linear OA(3228, 1029, F32, 14) (dual of [1029, 1001, 15]-code), using
(28−14, 28, 260)-Net in Base 32 — Constructive
(14, 28, 260)-net in base 32, using
- base change [i] based on (6, 20, 260)-net in base 128, using
- 4 times m-reduction [i] based on (6, 24, 260)-net in base 128, using
- base change [i] based on digital (3, 21, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 21, 260)-net over F256, using
- 4 times m-reduction [i] based on (6, 24, 260)-net in base 128, using
(28−14, 28, 515)-Net over F32 — Digital
Digital (14, 28, 515)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3228, 515, F32, 2, 14) (dual of [(515, 2), 1002, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3228, 1030, F32, 14) (dual of [1030, 1002, 15]-code), using
- construction XX applied to C1 = C([1021,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1021,11]) [i] based on
- linear OA(3225, 1023, F32, 13) (dual of [1023, 998, 14]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3227, 1023, F32, 14) (dual of [1023, 996, 15]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,11}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction XX applied to C1 = C([1021,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1021,11]) [i] based on
- OOA 2-folding [i] based on linear OA(3228, 1030, F32, 14) (dual of [1030, 1002, 15]-code), using
(28−14, 28, 114325)-Net in Base 32 — Upper bound on s
There is no (14, 28, 114326)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1 393805 449374 956868 998147 733209 890606 827528 > 3228 [i]