Best Known (66, 66+30, s)-Nets in Base 32
(66, 66+30, 2186)-Net over F32 — Constructive and digital
Digital (66, 96, 2186)-net over F32, using
- t-expansion [i] based on digital (65, 96, 2186)-net over F32, using
- net defined by OOA [i] based on linear OOA(3296, 2186, F32, 31, 31) (dual of [(2186, 31), 67670, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(3296, 32791, F32, 31) (dual of [32791, 32695, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3296, 32792, F32, 31) (dual of [32792, 32696, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(3291, 32769, F32, 31) (dual of [32769, 32678, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3273, 32769, F32, 25) (dual of [32769, 32696, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(325, 23, F32, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3296, 32792, F32, 31) (dual of [32792, 32696, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(3296, 32791, F32, 31) (dual of [32791, 32695, 32]-code), using
- net defined by OOA [i] based on linear OOA(3296, 2186, F32, 31, 31) (dual of [(2186, 31), 67670, 32]-NRT-code), using
(66, 66+30, 4369)-Net in Base 32 — Constructive
(66, 96, 4369)-net in base 32, using
- base change [i] based on digital (30, 60, 4369)-net over F256, using
- 1 times m-reduction [i] based on digital (30, 61, 4369)-net over F256, using
- net defined by OOA [i] based on linear OOA(25661, 4369, F256, 31, 31) (dual of [(4369, 31), 135378, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- OOA 15-folding and stacking with additional row [i] based on linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using
- net defined by OOA [i] based on linear OOA(25661, 4369, F256, 31, 31) (dual of [(4369, 31), 135378, 32]-NRT-code), using
- 1 times m-reduction [i] based on digital (30, 61, 4369)-net over F256, using
(66, 66+30, 36183)-Net over F32 — Digital
Digital (66, 96, 36183)-net over F32, using
(66, 66+30, large)-Net in Base 32 — Upper bound on s
There is no (66, 96, large)-net in base 32, because
- 28 times m-reduction [i] would yield (66, 68, large)-net in base 32, but