Best Known (82, 107, s)-Nets in Base 32
(82, 107, 87385)-Net over F32 — Constructive and digital
Digital (82, 107, 87385)-net over F32, using
- net defined by OOA [i] based on linear OOA(32107, 87385, F32, 25, 25) (dual of [(87385, 25), 2184518, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(32107, 1048621, F32, 25) (dual of [1048621, 1048514, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,7]) [i] based on
- linear OA(3297, 1048577, F32, 25) (dual of [1048577, 1048480, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3257, 1048577, F32, 15) (dual of [1048577, 1048520, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3210, 44, F32, 9) (dual of [44, 34, 10]-code), using
- extended algebraic-geometric code AGe(F,34P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- construction X applied to C([0,12]) ⊂ C([0,7]) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(32107, 1048621, F32, 25) (dual of [1048621, 1048514, 26]-code), using
(82, 107, 174763)-Net in Base 32 — Constructive
(82, 107, 174763)-net in base 32, using
- 322 times duplication [i] based on (80, 105, 174763)-net in base 32, using
- base change [i] based on digital (50, 75, 174763)-net over F128, using
- 1281 times duplication [i] based on digital (49, 74, 174763)-net over F128, using
- net defined by OOA [i] based on linear OOA(12874, 174763, F128, 25, 25) (dual of [(174763, 25), 4369001, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(12874, 2097157, F128, 25) (dual of [2097157, 2097083, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(12874, 2097160, F128, 25) (dual of [2097160, 2097086, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- linear OA(12873, 2097153, F128, 25) (dual of [2097153, 2097080, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12874, 2097160, F128, 25) (dual of [2097160, 2097086, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(12874, 2097157, F128, 25) (dual of [2097157, 2097083, 26]-code), using
- net defined by OOA [i] based on linear OOA(12874, 174763, F128, 25, 25) (dual of [(174763, 25), 4369001, 26]-NRT-code), using
- 1281 times duplication [i] based on digital (49, 74, 174763)-net over F128, using
- base change [i] based on digital (50, 75, 174763)-net over F128, using
(82, 107, 1623546)-Net over F32 — Digital
Digital (82, 107, 1623546)-net over F32, using
(82, 107, large)-Net in Base 32 — Upper bound on s
There is no (82, 107, large)-net in base 32, because
- 23 times m-reduction [i] would yield (82, 84, large)-net in base 32, but