Best Known (100−27, 100, s)-Nets in Base 32
(100−27, 100, 2619)-Net over F32 — Constructive and digital
Digital (73, 100, 2619)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 20, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (53, 80, 2521)-net over F32, using
- net defined by OOA [i] based on linear OOA(3280, 2521, F32, 27, 27) (dual of [(2521, 27), 67987, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3280, 32774, F32, 27) (dual of [32774, 32694, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3280, 32776, F32, 27) (dual of [32776, 32696, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(3279, 32769, F32, 27) (dual of [32769, 32690, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (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(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 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
- discarding factors / shortening the dual code based on linear OA(3280, 32776, F32, 27) (dual of [32776, 32696, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3280, 32774, F32, 27) (dual of [32774, 32694, 28]-code), using
- net defined by OOA [i] based on linear OOA(3280, 2521, F32, 27, 27) (dual of [(2521, 27), 67987, 28]-NRT-code), using
- digital (7, 20, 98)-net over F32, using
(100−27, 100, 20166)-Net in Base 32 — Constructive
(73, 100, 20166)-net in base 32, using
- 321 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
(100−27, 100, 209410)-Net over F32 — Digital
Digital (73, 100, 209410)-net over F32, using
(100−27, 100, large)-Net in Base 32 — Upper bound on s
There is no (73, 100, large)-net in base 32, because
- 25 times m-reduction [i] would yield (73, 75, large)-net in base 32, but