Best Known (79, 103, s)-Nets in Base 32
(79, 103, 87385)-Net over F32 — Constructive and digital
Digital (79, 103, 87385)-net over F32, using
- 321 times duplication [i] based on digital (78, 102, 87385)-net over F32, using
- net defined by OOA [i] based on linear OOA(32102, 87385, F32, 24, 24) (dual of [(87385, 24), 2097138, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(32102, 1048620, F32, 24) (dual of [1048620, 1048518, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(14) [i] based on
- linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(329, 44, F32, 8) (dual of [44, 35, 9]-code), using
- extended algebraic-geometric code AGe(F,35P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- construction X applied to Ce(23) ⊂ Ce(14) [i] based on
- OA 12-folding and stacking [i] based on linear OA(32102, 1048620, F32, 24) (dual of [1048620, 1048518, 25]-code), using
- net defined by OOA [i] based on linear OOA(32102, 87385, F32, 24, 24) (dual of [(87385, 24), 2097138, 25]-NRT-code), using
(79, 103, 174763)-Net in Base 32 — Constructive
(79, 103, 174763)-net in base 32, using
- 1 times m-reduction [i] based on (79, 104, 174763)-net in base 32, using
- net defined by OOA [i] based on OOA(32104, 174763, S32, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32104, 2097157, S32, 25), using
- discarding factors based on OA(32104, 2097160, S32, 25), using
- discarding parts of the base [i] 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 parts of the base [i] based on linear OA(12874, 2097160, F128, 25) (dual of [2097160, 2097086, 26]-code), using
- discarding factors based on OA(32104, 2097160, S32, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32104, 2097157, S32, 25), using
- net defined by OOA [i] based on OOA(32104, 174763, S32, 25, 25), using
(79, 103, 1673215)-Net over F32 — Digital
Digital (79, 103, 1673215)-net over F32, using
(79, 103, large)-Net in Base 32 — Upper bound on s
There is no (79, 103, large)-net in base 32, because
- 22 times m-reduction [i] would yield (79, 81, large)-net in base 32, but