Best Known (80−10, 80, s)-Nets in Base 2
(80−10, 80, 13107)-Net over F2 — Constructive and digital
Digital (70, 80, 13107)-net over F2, using
- net defined by OOA [i] based on linear OOA(280, 13107, F2, 10, 10) (dual of [(13107, 10), 130990, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(280, 65535, F2, 10) (dual of [65535, 65455, 11]-code), using
- 1 times truncation [i] based on linear OA(281, 65536, F2, 11) (dual of [65536, 65455, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 1 times truncation [i] based on linear OA(281, 65536, F2, 11) (dual of [65536, 65455, 12]-code), using
- OA 5-folding and stacking [i] based on linear OA(280, 65535, F2, 10) (dual of [65535, 65455, 11]-code), using
(80−10, 80, 21841)-Net over F2 — Digital
Digital (70, 80, 21841)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(280, 21841, F2, 3, 10) (dual of [(21841, 3), 65443, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(280, 21845, F2, 3, 10) (dual of [(21845, 3), 65455, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(280, 65535, F2, 10) (dual of [65535, 65455, 11]-code), using
- 1 times truncation [i] based on linear OA(281, 65536, F2, 11) (dual of [65536, 65455, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 1 times truncation [i] based on linear OA(281, 65536, F2, 11) (dual of [65536, 65455, 12]-code), using
- OOA 3-folding [i] based on linear OA(280, 65535, F2, 10) (dual of [65535, 65455, 11]-code), using
- discarding factors / shortening the dual code based on linear OOA(280, 21845, F2, 3, 10) (dual of [(21845, 3), 65455, 11]-NRT-code), using
(80−10, 80, 170725)-Net in Base 2 — Upper bound on s
There is no (70, 80, 170726)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 208943 793327 425921 368427 > 280 [i]