Best Known (104−23, 104, s)-Nets in Base 32
(104−23, 104, 95389)-Net over F32 — Constructive and digital
Digital (81, 104, 95389)-net over F32, using
- 321 times duplication [i] based on digital (80, 103, 95389)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 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 (66, 89, 95325)-net over F32, using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- digital (3, 14, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(104−23, 104, 190653)-Net in Base 32 — Constructive
(81, 104, 190653)-net in base 32, using
- net defined by OOA [i] based on OOA(32104, 190653, S32, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(32104, 2097184, S32, 23), using
- discarding parts of the base [i] based on linear OA(12874, 2097184, F128, 23) (dual of [2097184, 2097110, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,7]) [i] based on
- linear OA(12867, 2097153, F128, 23) (dual of [2097153, 2097086, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(12843, 2097153, F128, 15) (dual of [2097153, 2097110, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to C([0,11]) ⊂ C([0,7]) [i] based on
- discarding parts of the base [i] based on linear OA(12874, 2097184, F128, 23) (dual of [2097184, 2097110, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on OA(32104, 2097184, S32, 23), using
(104−23, 104, 3808439)-Net over F32 — Digital
Digital (81, 104, 3808439)-net over F32, using
(104−23, 104, large)-Net in Base 32 — Upper bound on s
There is no (81, 104, large)-net in base 32, because
- 21 times m-reduction [i] would yield (81, 83, large)-net in base 32, but