Best Known (128, 144, s)-Nets in Base 2
(128, 144, 32768)-Net over F2 — Constructive and digital
Digital (128, 144, 32768)-net over F2, using
- net defined by OOA [i] based on linear OOA(2144, 32768, F2, 16, 16) (dual of [(32768, 16), 524144, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2144, 262144, F2, 16) (dual of [262144, 262000, 17]-code), using
- 1 times truncation [i] based on linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(2144, 262144, F2, 16) (dual of [262144, 262000, 17]-code), using
(128, 144, 52428)-Net over F2 — Digital
Digital (128, 144, 52428)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2144, 52428, F2, 5, 16) (dual of [(52428, 5), 261996, 17]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2144, 262140, F2, 16) (dual of [262140, 261996, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2144, 262144, F2, 16) (dual of [262144, 262000, 17]-code), using
- 1 times truncation [i] based on linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2144, 262144, F2, 16) (dual of [262144, 262000, 17]-code), using
- OOA 5-folding [i] based on linear OA(2144, 262140, F2, 16) (dual of [262140, 261996, 17]-code), using
(128, 144, 986790)-Net in Base 2 — Upper bound on s
There is no (128, 144, 986791)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 22 300849 404479 749583 568974 995808 341813 921700 > 2144 [i]