Best Known (26, 47, s)-Nets in Base 32
(26, 47, 202)-Net over F32 — Constructive and digital
Digital (26, 47, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 17, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (9, 30, 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 (7, 17, 98)-net over F32, using
(26, 47, 322)-Net in Base 32 — Constructive
(26, 47, 322)-net in base 32, using
- (u, u+v)-construction [i] based on
- (2, 12, 65)-net in base 32, using
- base change [i] based on digital (0, 10, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base change [i] based on digital (0, 10, 65)-net over F64, using
- (14, 35, 257)-net in base 32, using
- 1 times m-reduction [i] based on (14, 36, 257)-net in base 32, using
- base change [i] based on (8, 30, 257)-net in base 64, using
- 2 times m-reduction [i] based on (8, 32, 257)-net in base 64, using
- base change [i] based on digital (0, 24, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 24, 257)-net over F256, using
- 2 times m-reduction [i] based on (8, 32, 257)-net in base 64, using
- base change [i] based on (8, 30, 257)-net in base 64, using
- 1 times m-reduction [i] based on (14, 36, 257)-net in base 32, using
- (2, 12, 65)-net in base 32, using
(26, 47, 1082)-Net over F32 — Digital
Digital (26, 47, 1082)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3247, 1082, F32, 21) (dual of [1082, 1035, 22]-code), using
- 49 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 11 times 0, 1, 33 times 0) [i] based on linear OA(3241, 1027, F32, 21) (dual of [1027, 986, 22]-code), using
- construction XX applied to C1 = C([1022,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([1022,19]) [i] based on
- linear OA(3239, 1023, F32, 20) (dual of [1023, 984, 21]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3239, 1023, F32, 20) (dual of [1023, 984, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3241, 1023, F32, 21) (dual of [1023, 982, 22]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3237, 1023, F32, 19) (dual of [1023, 986, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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([1022,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([1022,19]) [i] based on
- 49 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 11 times 0, 1, 33 times 0) [i] based on linear OA(3241, 1027, F32, 21) (dual of [1027, 986, 22]-code), using
(26, 47, 1225470)-Net in Base 32 — Upper bound on s
There is no (26, 47, 1225471)-net in base 32, because
- 1 times m-reduction [i] would yield (26, 46, 1225471)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1725 446032 357544 010026 224433 014422 622503 439179 424752 073714 657303 346411 > 3246 [i]