Best Known (35, 63, s)-Nets in Base 32
(35, 63, 224)-Net over F32 — Constructive and digital
Digital (35, 63, 224)-net over F32, using
- 2 times m-reduction [i] based on digital (35, 65, 224)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 24, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (11, 41, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (9, 24, 104)-net over F32, using
- (u, u+v)-construction [i] based on
(35, 63, 327)-Net in Base 32 — Constructive
(35, 63, 327)-net in base 32, using
- (u, u+v)-construction [i] based on
- (7, 21, 150)-net in base 32, using
- base change [i] based on digital (1, 15, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 15, 150)-net over F128, using
- (14, 42, 177)-net in base 32, using
- base change [i] based on digital (7, 35, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 35, 177)-net over F64, using
- (7, 21, 150)-net in base 32, using
(35, 63, 1188)-Net over F32 — Digital
Digital (35, 63, 1188)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3263, 1188, F32, 28) (dual of [1188, 1125, 29]-code), using
- 153 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 6 times 0, 1, 17 times 0, 1, 41 times 0, 1, 82 times 0) [i] based on linear OA(3255, 1027, F32, 28) (dual of [1027, 972, 29]-code), using
- construction XX applied to C1 = C([1022,25]), C2 = C([0,26]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([1022,26]) [i] based on
- linear OA(3253, 1023, F32, 27) (dual of [1023, 970, 28]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,25}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3253, 1023, F32, 27) (dual of [1023, 970, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3255, 1023, F32, 28) (dual of [1023, 968, 29]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,26}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3251, 1023, F32, 26) (dual of [1023, 972, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,25]), C2 = C([0,26]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([1022,26]) [i] based on
- 153 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 6 times 0, 1, 17 times 0, 1, 41 times 0, 1, 82 times 0) [i] based on linear OA(3255, 1027, F32, 28) (dual of [1027, 972, 29]-code), using
(35, 63, 1156826)-Net in Base 32 — Upper bound on s
There is no (35, 63, 1156827)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 66749 762900 438792 768341 943574 298742 864422 586001 629355 823969 494392 880207 902723 864219 235020 012532 > 3263 [i]