Best Known (101−27, 101, s)-Nets in Base 32
(101−27, 101, 2624)-Net over F32 — Constructive and digital
Digital (74, 101, 2624)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 22, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (52, 79, 2520)-net over F32, using
- net defined by OOA [i] based on linear OOA(3279, 2520, F32, 27, 27) (dual of [(2520, 27), 67961, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3279, 32761, F32, 27) (dual of [32761, 32682, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3279, 32761, F32, 27) (dual of [32761, 32682, 28]-code), using
- net defined by OOA [i] based on linear OOA(3279, 2520, F32, 27, 27) (dual of [(2520, 27), 67961, 28]-NRT-code), using
- digital (9, 22, 104)-net over F32, using
(101−27, 101, 20166)-Net in Base 32 — Constructive
(74, 101, 20166)-net in base 32, using
- 322 times duplication [i] based on (72, 99, 20166)-net in base 32, using
- net defined by OOA [i] based on OOA(3299, 20166, S32, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(3299, 262159, S32, 27), using
- discarding factors based on OA(3299, 262160, S32, 27), using
- discarding parts of the base [i] based on linear OA(6482, 262160, F64, 27) (dual of [262160, 262078, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [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(6467, 262145, F64, 23) (dual of [262145, 262078, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(643, 15, F64, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,64) or 15-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] based on
- discarding parts of the base [i] based on linear OA(6482, 262160, F64, 27) (dual of [262160, 262078, 28]-code), using
- discarding factors based on OA(3299, 262160, S32, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(3299, 262159, S32, 27), using
- net defined by OOA [i] based on OOA(3299, 20166, S32, 27, 27), using
(101−27, 101, 239267)-Net over F32 — Digital
Digital (74, 101, 239267)-net over F32, using
(101−27, 101, large)-Net in Base 32 — Upper bound on s
There is no (74, 101, large)-net in base 32, because
- 25 times m-reduction [i] would yield (74, 76, large)-net in base 32, but