Best Known (75, 75+35, s)-Nets in Base 32
(75, 75+35, 1929)-Net over F32 — Constructive and digital
Digital (75, 110, 1929)-net over F32, using
- 323 times duplication [i] based on digital (72, 107, 1929)-net over F32, using
- net defined by OOA [i] based on linear OOA(32107, 1929, F32, 35, 35) (dual of [(1929, 35), 67408, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32107, 32794, F32, 35) (dual of [32794, 32687, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(32107, 32796, F32, 35) (dual of [32796, 32689, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(26) [i] based on
- linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(327, 28, F32, 7) (dual of [28, 21, 8]-code or 28-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- construction X applied to Ce(34) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(32107, 32796, F32, 35) (dual of [32796, 32689, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32107, 32794, F32, 35) (dual of [32794, 32687, 36]-code), using
- net defined by OOA [i] based on linear OOA(32107, 1929, F32, 35, 35) (dual of [(1929, 35), 67408, 36]-NRT-code), using
(75, 75+35, 32805)-Net over F32 — Digital
Digital (75, 110, 32805)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32110, 32805, F32, 35) (dual of [32805, 32695, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(24) [i] based on
- linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3273, 32768, F32, 25) (dual of [32768, 32695, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3210, 37, F32, 9) (dual of [37, 27, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, 43, F32, 9) (dual of [43, 33, 10]-code), using
- algebraic-geometric code AG(F,33P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- discarding factors / shortening the dual code based on linear OA(3210, 43, F32, 9) (dual of [43, 33, 10]-code), using
- construction X applied to Ce(34) ⊂ Ce(24) [i] based on
(75, 75+35, large)-Net in Base 32 — Upper bound on s
There is no (75, 110, large)-net in base 32, because
- 33 times m-reduction [i] would yield (75, 77, large)-net in base 32, but