Best Known (102, 102+22, s)-Nets in Base 2
(102, 102+22, 265)-Net over F2 — Constructive and digital
Digital (102, 124, 265)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 5)-net over F2, using
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- digital (90, 112, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 28, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 28, 65)-net over F16, using
- digital (1, 12, 5)-net over F2, using
(102, 102+22, 687)-Net over F2 — Digital
Digital (102, 124, 687)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2124, 687, F2, 3, 22) (dual of [(687, 3), 1937, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2124, 2061, F2, 22) (dual of [2061, 1937, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2122, 2059, F2, 22) (dual of [2059, 1937, 23]-code), using
- 1 times truncation [i] based on linear OA(2123, 2060, F2, 23) (dual of [2060, 1937, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2111, 2048, F2, 21) (dual of [2048, 1937, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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 X applied to Ce(22) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2123, 2060, F2, 23) (dual of [2060, 1937, 24]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2122, 2059, F2, 22) (dual of [2059, 1937, 23]-code), using
- OOA 3-folding [i] based on linear OA(2124, 2061, F2, 22) (dual of [2061, 1937, 23]-code), using
(102, 102+22, 12130)-Net in Base 2 — Upper bound on s
There is no (102, 124, 12131)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 21 281385 931546 030997 955831 614466 745336 > 2124 [i]