Best Known (100−20, 100, s)-Nets in Base 2
(100−20, 100, 196)-Net over F2 — Constructive and digital
Digital (80, 100, 196)-net over F2, using
- trace code for nets [i] based on digital (5, 25, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
(100−20, 100, 367)-Net over F2 — Digital
Digital (80, 100, 367)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2100, 367, F2, 2, 20) (dual of [(367, 2), 634, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2100, 512, F2, 2, 20) (dual of [(512, 2), 924, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2100, 1024, F2, 20) (dual of [1024, 924, 21]-code), using
- 1 times truncation [i] based on linear OA(2101, 1025, F2, 21) (dual of [1025, 924, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2101, 1025, F2, 21) (dual of [1025, 924, 22]-code), using
- OOA 2-folding [i] based on linear OA(2100, 1024, F2, 20) (dual of [1024, 924, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(2100, 512, F2, 2, 20) (dual of [(512, 2), 924, 21]-NRT-code), using
(100−20, 100, 4622)-Net in Base 2 — Upper bound on s
There is no (80, 100, 4623)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 267818 886653 277131 000988 321901 > 2100 [i]