Best Known (160−27, 160, s)-Nets in Base 8
(160−27, 160, 40331)-Net over F8 — Constructive and digital
Digital (133, 160, 40331)-net over F8, using
- net defined by OOA [i] based on linear OOA(8160, 40331, F8, 27, 27) (dual of [(40331, 27), 1088777, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8160, 524304, F8, 27) (dual of [524304, 524144, 28]-code), using
- trace code [i] based on linear OA(6480, 262152, F64, 27) (dual of [262152, 262072, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(6479, 262145, F64, 27) (dual of [262145, 262066, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(6473, 262145, F64, 25) (dual of [262145, 262072, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- trace code [i] based on linear OA(6480, 262152, F64, 27) (dual of [262152, 262072, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8160, 524304, F8, 27) (dual of [524304, 524144, 28]-code), using
(160−27, 160, 544104)-Net over F8 — Digital
Digital (133, 160, 544104)-net over F8, using
(160−27, 160, large)-Net in Base 8 — Upper bound on s
There is no (133, 160, large)-net in base 8, because
- 25 times m-reduction [i] would yield (133, 135, large)-net in base 8, but