Best Known (34, 34+14, s)-Nets in Base 32
(34, 34+14, 4725)-Net over F32 — Constructive and digital
Digital (34, 48, 4725)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 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 (26, 40, 4681)-net over F32, using
- net defined by OOA [i] based on linear OOA(3240, 4681, F32, 14, 14) (dual of [(4681, 14), 65494, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3240, 32767, F32, 14) (dual of [32767, 32727, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3240, 32767, F32, 14) (dual of [32767, 32727, 15]-code), using
- net defined by OOA [i] based on linear OOA(3240, 4681, F32, 14, 14) (dual of [(4681, 14), 65494, 15]-NRT-code), using
- digital (1, 8, 44)-net over F32, using
(34, 34+14, 37449)-Net in Base 32 — Constructive
(34, 48, 37449)-net in base 32, using
- base change [i] based on digital (26, 40, 37449)-net over F64, using
- net defined by OOA [i] based on linear OOA(6440, 37449, F64, 14, 14) (dual of [(37449, 14), 524246, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(6440, 262143, F64, 14) (dual of [262143, 262103, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(6440, 262143, F64, 14) (dual of [262143, 262103, 15]-code), using
- net defined by OOA [i] based on linear OOA(6440, 37449, F64, 14, 14) (dual of [(37449, 14), 524246, 15]-NRT-code), using
(34, 34+14, 66003)-Net over F32 — Digital
Digital (34, 48, 66003)-net over F32, using
(34, 34+14, 131073)-Net in Base 32
(34, 48, 131073)-net in base 32, using
- base change [i] based on digital (26, 40, 131073)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6440, 131073, F64, 2, 14) (dual of [(131073, 2), 262106, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6440, 262146, F64, 14) (dual of [262146, 262106, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6440, 262147, F64, 14) (dual of [262147, 262107, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(6440, 262147, F64, 14) (dual of [262147, 262107, 15]-code), using
- OOA 2-folding [i] based on linear OA(6440, 262146, F64, 14) (dual of [262146, 262106, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6440, 131073, F64, 2, 14) (dual of [(131073, 2), 262106, 15]-NRT-code), using
(34, 34+14, large)-Net in Base 32 — Upper bound on s
There is no (34, 48, large)-net in base 32, because
- 12 times m-reduction [i] would yield (34, 36, large)-net in base 32, but