Best Known (17, 21, s)-Nets in Base 2
(17, 21, 1025)-Net over F2 — Constructive and digital
Digital (17, 21, 1025)-net over F2, using
(17, 21, 1035)-Net over F2 — Digital
Digital (17, 21, 1035)-net over F2, using
- net defined by OOA [i] based on linear OOA(221, 1035, F2, 4, 4) (dual of [(1035, 4), 4119, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(221, 1035, F2, 3, 4) (dual of [(1035, 3), 3084, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(221, 1035, F2, 4) (dual of [1035, 1014, 5]-code), using
- 1 times truncation [i] based on linear OA(222, 1036, F2, 5) (dual of [1036, 1014, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(221, 1024, F2, 5) (dual of [1024, 1003, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(211, 1024, F2, 3) (dual of [1024, 1013, 4]-code or 1024-cap in PG(10,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(211, 12, F2, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,2)), using
- dual of repetition code with length 12 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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(222, 1036, F2, 5) (dual of [1036, 1014, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(221, 1035, F2, 4) (dual of [1035, 1014, 5]-code), using
- appending kth column [i] based on linear OOA(221, 1035, F2, 3, 4) (dual of [(1035, 3), 3084, 5]-NRT-code), using
(17, 21, 2045)-Net in Base 2 — Upper bound on s
There is no (17, 21, 2046)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2 098174 > 221 [i]