Best Known (125, 153, s)-Nets in Base 2
(125, 153, 267)-Net over F2 — Constructive and digital
Digital (125, 153, 267)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 7)-net over F2, using
- net from sequence [i] based on digital (3, 6)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 3 and N(F) ≥ 7, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (3, 6)-sequence over F2, using
- digital (108, 136, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 34, 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, 34, 65)-net over F16, using
- digital (3, 17, 7)-net over F2, using
(125, 153, 573)-Net over F2 — Digital
Digital (125, 153, 573)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2153, 573, F2, 28) (dual of [573, 420, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2153, 1070, F2, 28) (dual of [1070, 917, 29]-code), using
- construction XX applied to C1 = C([1017,20]), C2 = C([0,22]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1017,22]) [i] based on
- linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−6,−5,…,20}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2111, 1023, F2, 23) (dual of [1023, 912, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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 = {−6,−5,…,22}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 44, F2, 4) (dual of [44, 33, 5]-code), using
- 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
- construction XX applied to C1 = C([1017,20]), C2 = C([0,22]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1017,22]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2153, 1070, F2, 28) (dual of [1070, 917, 29]-code), using
(125, 153, 11763)-Net in Base 2 — Upper bound on s
There is no (125, 153, 11764)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 11427 193524 452108 913669 071479 385031 194298 860036 > 2153 [i]