Best Known (252−36, 252, s)-Nets in Base 2
(252−36, 252, 910)-Net over F2 — Constructive and digital
Digital (216, 252, 910)-net over F2, using
- net defined by OOA [i] based on linear OOA(2252, 910, F2, 36, 36) (dual of [(910, 36), 32508, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(2252, 16380, F2, 36) (dual of [16380, 16128, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2252, 16384, F2, 36) (dual of [16384, 16132, 37]-code), using
- 1 times truncation [i] based on linear OA(2253, 16385, F2, 37) (dual of [16385, 16132, 38]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2253, 16385, F2, 37) (dual of [16385, 16132, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2252, 16384, F2, 36) (dual of [16384, 16132, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(2252, 16380, F2, 36) (dual of [16380, 16128, 37]-code), using
(252−36, 252, 3276)-Net over F2 — Digital
Digital (216, 252, 3276)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2252, 3276, F2, 5, 36) (dual of [(3276, 5), 16128, 37]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2252, 16380, F2, 36) (dual of [16380, 16128, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2252, 16384, F2, 36) (dual of [16384, 16132, 37]-code), using
- 1 times truncation [i] based on linear OA(2253, 16385, F2, 37) (dual of [16385, 16132, 38]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2253, 16385, F2, 37) (dual of [16385, 16132, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2252, 16384, F2, 36) (dual of [16384, 16132, 37]-code), using
- OOA 5-folding [i] based on linear OA(2252, 16380, F2, 36) (dual of [16380, 16128, 37]-code), using
(252−36, 252, 123724)-Net in Base 2 — Upper bound on s
There is no (216, 252, 123725)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 7237 145569 012323 631437 142884 540616 527203 541916 422799 116473 419634 659131 021656 > 2252 [i]