Best Known (215, 215+22, s)-Nets in Base 2
(215, 215+22, 190653)-Net over F2 — Constructive and digital
Digital (215, 237, 190653)-net over F2, using
- net defined by OOA [i] based on linear OOA(2237, 190653, F2, 22, 22) (dual of [(190653, 22), 4194129, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2237, 2097183, F2, 22) (dual of [2097183, 2096946, 23]-code), using
- 1 times truncation [i] based on linear OA(2238, 2097184, F2, 23) (dual of [2097184, 2096946, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2190, 2097152, F2, 19) (dual of [2097152, 2096962, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2238, 2097184, F2, 23) (dual of [2097184, 2096946, 24]-code), using
- OA 11-folding and stacking [i] based on linear OA(2237, 2097183, F2, 22) (dual of [2097183, 2096946, 23]-code), using
(215, 215+22, 299597)-Net over F2 — Digital
Digital (215, 237, 299597)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2237, 299597, F2, 7, 22) (dual of [(299597, 7), 2096942, 23]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2237, 2097179, F2, 22) (dual of [2097179, 2096942, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2237, 2097183, F2, 22) (dual of [2097183, 2096946, 23]-code), using
- 1 times truncation [i] based on linear OA(2238, 2097184, F2, 23) (dual of [2097184, 2096946, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2190, 2097152, F2, 19) (dual of [2097152, 2096962, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2238, 2097184, F2, 23) (dual of [2097184, 2096946, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2237, 2097183, F2, 22) (dual of [2097183, 2096946, 23]-code), using
- OOA 7-folding [i] based on linear OA(2237, 2097179, F2, 22) (dual of [2097179, 2096942, 23]-code), using
(215, 215+22, large)-Net in Base 2 — Upper bound on s
There is no (215, 237, large)-net in base 2, because
- 20 times m-reduction [i] would yield (215, 217, large)-net in base 2, but