Best Known (15, 19, s)-Nets in Base 2
(15, 19, 513)-Net over F2 — Constructive and digital
Digital (15, 19, 513)-net over F2, using
(15, 19, 522)-Net over F2 — Digital
Digital (15, 19, 522)-net over F2, using
- net defined by OOA [i] based on linear OOA(219, 522, F2, 4, 4) (dual of [(522, 4), 2069, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(219, 522, F2, 3, 4) (dual of [(522, 3), 1547, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(219, 522, F2, 4) (dual of [522, 503, 5]-code), using
- 1 times truncation [i] based on linear OA(220, 523, F2, 5) (dual of [523, 503, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(219, 512, F2, 5) (dual of [512, 493, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(210, 512, F2, 3) (dual of [512, 502, 4]-code or 512-cap in PG(9,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(210, 11, F2, 9) (dual of [11, 1, 10]-code), using
- strength reduction [i] based on linear OA(210, 11, F2, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
- dual of repetition code with length 11 [i]
- strength reduction [i] based on linear OA(210, 11, F2, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- 1 times truncation [i] based on linear OA(220, 523, F2, 5) (dual of [523, 503, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(219, 522, F2, 4) (dual of [522, 503, 5]-code), using
- appending kth column [i] based on linear OOA(219, 522, F2, 3, 4) (dual of [(522, 3), 1547, 5]-NRT-code), using
(15, 19, 1021)-Net in Base 2 — Upper bound on s
There is no (15, 19, 1022)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 524798 > 219 [i]