Best Known (49, 67, s)-Nets in Base 32
(49, 67, 3729)-Net over F32 — Constructive and digital
Digital (49, 67, 3729)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (6, 15, 88)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 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 (1, 10, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32 (see above)
- digital (1, 5, 44)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (34, 52, 3641)-net over F32, using
- net defined by OOA [i] based on linear OOA(3252, 3641, F32, 18, 18) (dual of [(3641, 18), 65486, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3252, 32769, F32, 18) (dual of [32769, 32717, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3252, 32771, F32, 18) (dual of [32771, 32719, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- 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(3249, 32768, F32, 17) (dual of [32768, 32719, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3252, 32771, F32, 18) (dual of [32771, 32719, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(3252, 32769, F32, 18) (dual of [32769, 32717, 19]-code), using
- net defined by OOA [i] based on linear OOA(3252, 3641, F32, 18, 18) (dual of [(3641, 18), 65486, 19]-NRT-code), using
- digital (6, 15, 88)-net over F32, using
(49, 67, 29128)-Net in Base 32 — Constructive
(49, 67, 29128)-net in base 32, using
- 321 times duplication [i] based on (48, 66, 29128)-net in base 32, using
- base change [i] based on digital (37, 55, 29128)-net over F64, using
- 641 times duplication [i] based on digital (36, 54, 29128)-net over F64, using
- net defined by OOA [i] based on linear OOA(6454, 29128, F64, 18, 18) (dual of [(29128, 18), 524250, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(6454, 262152, F64, 18) (dual of [262152, 262098, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(6454, 262155, F64, 18) (dual of [262155, 262101, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- 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(6443, 262144, F64, 15) (dual of [262144, 262101, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(6454, 262155, F64, 18) (dual of [262155, 262101, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(6454, 262152, F64, 18) (dual of [262152, 262098, 19]-code), using
- net defined by OOA [i] based on linear OOA(6454, 29128, F64, 18, 18) (dual of [(29128, 18), 524250, 19]-NRT-code), using
- 641 times duplication [i] based on digital (36, 54, 29128)-net over F64, using
- base change [i] based on digital (37, 55, 29128)-net over F64, using
(49, 67, 197999)-Net over F32 — Digital
Digital (49, 67, 197999)-net over F32, using
(49, 67, large)-Net in Base 32 — Upper bound on s
There is no (49, 67, large)-net in base 32, because
- 16 times m-reduction [i] would yield (49, 51, large)-net in base 32, but