Best Known (85, 85+25, s)-Nets in Base 32
(85, 85+25, 87425)-Net over F32 — Constructive and digital
Digital (85, 110, 87425)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (72, 97, 87381)-net over F32, using
- net defined by OOA [i] based on linear OOA(3297, 87381, F32, 25, 25) (dual of [(87381, 25), 2184428, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3297, 1048573, F32, 25) (dual of [1048573, 1048476, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3297, 1048573, F32, 25) (dual of [1048573, 1048476, 26]-code), using
- net defined by OOA [i] based on linear OOA(3297, 87381, F32, 25, 25) (dual of [(87381, 25), 2184428, 26]-NRT-code), using
- digital (1, 13, 44)-net over F32, using
(85, 85+25, 174764)-Net in Base 32 — Constructive
(85, 110, 174764)-net in base 32, using
- 322 times duplication [i] based on (83, 108, 174764)-net in base 32, using
- net defined by OOA [i] based on OOA(32108, 174764, S32, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32108, 2097169, S32, 25), using
- discarding factors based on OA(32108, 2097171, S32, 25), using
- discarding parts of the base [i] based on linear OA(12877, 2097171, F128, 25) (dual of [2097171, 2097094, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(12877, 2097171, F128, 25) (dual of [2097171, 2097094, 26]-code), using
- discarding factors based on OA(32108, 2097171, S32, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32108, 2097169, S32, 25), using
- net defined by OOA [i] based on OOA(32108, 174764, S32, 25, 25), using
(85, 85+25, 2503844)-Net over F32 — Digital
Digital (85, 110, 2503844)-net over F32, using
(85, 85+25, large)-Net in Base 32 — Upper bound on s
There is no (85, 110, large)-net in base 32, because
- 23 times m-reduction [i] would yield (85, 87, large)-net in base 32, but