Best Known (104−33, 104, s)-Nets in Base 32
(104−33, 104, 2050)-Net over F32 — Constructive and digital
Digital (71, 104, 2050)-net over F32, using
- 321 times duplication [i] based on digital (70, 103, 2050)-net over F32, using
- net defined by OOA [i] based on linear OOA(32103, 2050, F32, 33, 33) (dual of [(2050, 33), 67547, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(32103, 32801, F32, 33) (dual of [32801, 32698, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(32103, 32802, F32, 33) (dual of [32802, 32699, 34]-code), using
- construction XX applied to Ce(32) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(328, 33, F32, 8) (dual of [33, 25, 9]-code or 33-arc in PG(7,32)), using
- extended Reed–Solomon code RSe(25,32) [i]
- linear OA(320, 1, F32, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(32) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(32103, 32802, F32, 33) (dual of [32802, 32699, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(32103, 32801, F32, 33) (dual of [32801, 32698, 34]-code), using
- net defined by OOA [i] based on linear OOA(32103, 2050, F32, 33, 33) (dual of [(2050, 33), 67547, 34]-NRT-code), using
(104−33, 104, 4096)-Net in Base 32 — Constructive
(71, 104, 4096)-net in base 32, using
- base change [i] based on digital (32, 65, 4096)-net over F256, using
- net defined by OOA [i] based on linear OOA(25665, 4096, F256, 33, 33) (dual of [(4096, 33), 135103, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- net defined by OOA [i] based on linear OOA(25665, 4096, F256, 33, 33) (dual of [(4096, 33), 135103, 34]-NRT-code), using
(104−33, 104, 32805)-Net over F32 — Digital
Digital (71, 104, 32805)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32104, 32805, F32, 33) (dual of [32805, 32701, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(22) [i] based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3210, 37, F32, 9) (dual of [37, 27, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, 43, F32, 9) (dual of [43, 33, 10]-code), using
- algebraic-geometric code AG(F,33P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- discarding factors / shortening the dual code based on linear OA(3210, 43, F32, 9) (dual of [43, 33, 10]-code), using
- construction X applied to Ce(32) ⊂ Ce(22) [i] based on
(104−33, 104, large)-Net in Base 32 — Upper bound on s
There is no (71, 104, large)-net in base 32, because
- 31 times m-reduction [i] would yield (71, 73, large)-net in base 32, but