Best Known (42−12, 42, s)-Nets in Base 32
(42−12, 42, 5506)-Net over F32 — Constructive and digital
Digital (30, 42, 5506)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (23, 35, 5462)-net over F32, using
- net defined by OOA [i] based on linear OOA(3235, 5462, F32, 12, 12) (dual of [(5462, 12), 65509, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3235, 32772, F32, 12) (dual of [32772, 32737, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3235, 32775, F32, 12) (dual of [32775, 32740, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(3234, 32768, F32, 12) (dual of [32768, 32734, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3228, 32768, F32, 10) (dual of [32768, 32740, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3235, 32775, F32, 12) (dual of [32775, 32740, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3235, 32772, F32, 12) (dual of [32772, 32737, 13]-code), using
- net defined by OOA [i] based on linear OOA(3235, 5462, F32, 12, 12) (dual of [(5462, 12), 65509, 13]-NRT-code), using
- digital (1, 7, 44)-net over F32, using
(42−12, 42, 43691)-Net in Base 32 — Constructive
(30, 42, 43691)-net in base 32, using
- base change [i] based on digital (23, 35, 43691)-net over F64, using
- 641 times duplication [i] based on digital (22, 34, 43691)-net over F64, using
- net defined by OOA [i] based on linear OOA(6434, 43691, F64, 12, 12) (dual of [(43691, 12), 524258, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(6434, 262146, F64, 12) (dual of [262146, 262112, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(6434, 262146, F64, 12) (dual of [262146, 262112, 13]-code), using
- net defined by OOA [i] based on linear OOA(6434, 43691, F64, 12, 12) (dual of [(43691, 12), 524258, 13]-NRT-code), using
- 641 times duplication [i] based on digital (22, 34, 43691)-net over F64, using
(42−12, 42, 88433)-Net over F32 — Digital
Digital (30, 42, 88433)-net over F32, using
(42−12, 42, 131075)-Net in Base 32
(30, 42, 131075)-net in base 32, using
- base change [i] based on digital (23, 35, 131075)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6435, 131075, F64, 2, 12) (dual of [(131075, 2), 262115, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6435, 262150, F64, 12) (dual of [262150, 262115, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6435, 262151, F64, 12) (dual of [262151, 262116, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(6435, 262151, F64, 12) (dual of [262151, 262116, 13]-code), using
- OOA 2-folding [i] based on linear OA(6435, 262150, F64, 12) (dual of [262150, 262115, 13]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6435, 131075, F64, 2, 12) (dual of [(131075, 2), 262115, 13]-NRT-code), using
(42−12, 42, large)-Net in Base 32 — Upper bound on s
There is no (30, 42, large)-net in base 32, because
- 10 times m-reduction [i] would yield (30, 32, large)-net in base 32, but