Best Known (35, 61, s)-Nets in Base 32
(35, 61, 240)-Net over F32 — Constructive and digital
Digital (35, 61, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 24, 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 (11, 37, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 24, 120)-net over F32, using
(35, 61, 386)-Net in Base 32 — Constructive
(35, 61, 386)-net in base 32, using
- (u, u+v)-construction [i] based on
- (6, 19, 129)-net in base 32, using
- 2 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
- base change [i] based on digital (0, 15, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 15, 129)-net over F128, using
- 2 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
- (16, 42, 257)-net in base 32, using
- base change [i] based on (9, 35, 257)-net in base 64, using
- 1 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
- base change [i] based on digital (0, 27, 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, 27, 257)-net over F256, using
- 1 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
- base change [i] based on (9, 35, 257)-net in base 64, using
- (6, 19, 129)-net in base 32, using
(35, 61, 1558)-Net over F32 — Digital
Digital (35, 61, 1558)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3261, 1558, F32, 26) (dual of [1558, 1497, 27]-code), using
- 521 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 7 times 0, 1, 21 times 0, 1, 47 times 0, 1, 94 times 0, 1, 150 times 0, 1, 193 times 0) [i] based on linear OA(3251, 1027, F32, 26) (dual of [1027, 976, 27]-code), using
- construction XX applied to C1 = C([1022,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([1022,24]) [i] based on
- linear OA(3249, 1023, F32, 25) (dual of [1023, 974, 26]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3249, 1023, F32, 25) (dual of [1023, 974, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3251, 1023, F32, 26) (dual of [1023, 972, 27]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3247, 1023, F32, 24) (dual of [1023, 976, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [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([1022,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([1022,24]) [i] based on
- 521 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 7 times 0, 1, 21 times 0, 1, 47 times 0, 1, 94 times 0, 1, 150 times 0, 1, 193 times 0) [i] based on linear OA(3251, 1027, F32, 26) (dual of [1027, 976, 27]-code), using
(35, 61, 2111883)-Net in Base 32 — Upper bound on s
There is no (35, 61, 2111884)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 65 185296 234452 288657 450859 312688 883820 242114 639410 390679 303896 679546 901656 503396 649457 317024 > 3261 [i]