Best Known (55, 55+20, s)-Nets in Base 32
(55, 55+20, 3375)-Net over F32 — Constructive and digital
Digital (55, 75, 3375)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 17, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (38, 58, 3277)-net over F32, using
- net defined by OOA [i] based on linear OOA(3258, 3277, F32, 20, 20) (dual of [(3277, 20), 65482, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3258, 32770, F32, 20) (dual of [32770, 32712, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3258, 32771, F32, 20) (dual of [32771, 32713, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3258, 32771, F32, 20) (dual of [32771, 32713, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3258, 32770, F32, 20) (dual of [32770, 32712, 21]-code), using
- net defined by OOA [i] based on linear OOA(3258, 3277, F32, 20, 20) (dual of [(3277, 20), 65482, 21]-NRT-code), using
- digital (7, 17, 98)-net over F32, using
(55, 55+20, 26216)-Net in Base 32 — Constructive
(55, 75, 26216)-net in base 32, using
- net defined by OOA [i] based on OOA(3275, 26216, S32, 20, 20), using
- OA 10-folding and stacking [i] based on OA(3275, 262160, S32, 20), using
- discarding factors based on OA(3275, 262163, S32, 20), using
- discarding parts of the base [i] based on linear OA(6462, 262163, F64, 20) (dual of [262163, 262101, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(6462, 262163, F64, 20) (dual of [262163, 262101, 21]-code), using
- discarding factors based on OA(3275, 262163, S32, 20), using
- OA 10-folding and stacking [i] based on OA(3275, 262160, S32, 20), using
(55, 55+20, 223488)-Net over F32 — Digital
Digital (55, 75, 223488)-net over F32, using
(55, 55+20, large)-Net in Base 32 — Upper bound on s
There is no (55, 75, large)-net in base 32, because
- 18 times m-reduction [i] would yield (55, 57, large)-net in base 32, but