Best Known (122, 152, s)-Nets in Base 2
(122, 152, 260)-Net over F2 — Constructive and digital
Digital (122, 152, 260)-net over F2, using
- t-expansion [i] based on digital (120, 152, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 38, 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, 38, 65)-net over F16, using
(122, 152, 476)-Net over F2 — Digital
Digital (122, 152, 476)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, 476, F2, 2, 30) (dual of [(476, 2), 800, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2152, 522, F2, 2, 30) (dual of [(522, 2), 892, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2152, 1044, F2, 30) (dual of [1044, 892, 31]-code), using
- 1 times truncation [i] based on linear OA(2153, 1045, F2, 31) (dual of [1045, 892, 32]-code), using
- construction XX applied to C1 = C([1021,26]), C2 = C([0,28]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([1021,28]) [i] based on
- linear OA(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code) (see above)
- construction XX applied to C1 = C([1021,26]), C2 = C([0,28]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([1021,28]) [i] based on
- 1 times truncation [i] based on linear OA(2153, 1045, F2, 31) (dual of [1045, 892, 32]-code), using
- OOA 2-folding [i] based on linear OA(2152, 1044, F2, 30) (dual of [1044, 892, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(2152, 522, F2, 2, 30) (dual of [(522, 2), 892, 31]-NRT-code), using
(122, 152, 7192)-Net in Base 2 — Upper bound on s
There is no (122, 152, 7193)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5715 023487 142141 089231 166414 582658 163985 137408 > 2152 [i]