Best Known (47, 47+19, s)-Nets in Base 32
(47, 47+19, 3685)-Net over F32 — Constructive and digital
Digital (47, 66, 3685)-net over F32, using
- 321 times duplication [i] based on digital (46, 65, 3685)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 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 (36, 55, 3641)-net over F32, using
- net defined by OOA [i] based on linear OOA(3255, 3641, F32, 19, 19) (dual of [(3641, 19), 69124, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3255, 32770, F32, 19) (dual of [32770, 32715, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3255, 32771, F32, 19) (dual of [32771, 32716, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(3255, 32768, F32, 19) (dual of [32768, 32713, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3252, 32768, F32, 18) (dual of [32768, 32716, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 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
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(3255, 32771, F32, 19) (dual of [32771, 32716, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3255, 32770, F32, 19) (dual of [32770, 32715, 20]-code), using
- net defined by OOA [i] based on linear OOA(3255, 3641, F32, 19, 19) (dual of [(3641, 19), 69124, 20]-NRT-code), using
- digital (1, 10, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(47, 47+19, 29127)-Net in Base 32 — Constructive
(47, 66, 29127)-net in base 32, using
- base change [i] based on digital (36, 55, 29127)-net over F64, using
- net defined by OOA [i] based on linear OOA(6455, 29127, F64, 19, 19) (dual of [(29127, 19), 553358, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using
- net defined by OOA [i] based on linear OOA(6455, 29127, F64, 19, 19) (dual of [(29127, 19), 553358, 20]-NRT-code), using
(47, 47+19, 80482)-Net over F32 — Digital
Digital (47, 66, 80482)-net over F32, using
(47, 47+19, 103786)-Net in Base 32
(47, 66, 103786)-net in base 32, using
- base change [i] based on digital (36, 55, 103786)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6455, 103786, F64, 2, 19) (dual of [(103786, 2), 207517, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6455, 131073, F64, 2, 19) (dual of [(131073, 2), 262091, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6455, 262146, F64, 19) (dual of [262146, 262091, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(6455, 262147, F64, 19) (dual of [262147, 262092, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(6455, 262147, F64, 19) (dual of [262147, 262092, 20]-code), using
- OOA 2-folding [i] based on linear OA(6455, 262146, F64, 19) (dual of [262146, 262091, 20]-code), using
- discarding factors / shortening the dual code based on linear OOA(6455, 131073, F64, 2, 19) (dual of [(131073, 2), 262091, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6455, 103786, F64, 2, 19) (dual of [(103786, 2), 207517, 20]-NRT-code), using
(47, 47+19, large)-Net in Base 32 — Upper bound on s
There is no (47, 66, large)-net in base 32, because
- 17 times m-reduction [i] would yield (47, 49, large)-net in base 32, but