Best Known (76, 76+27, s)-Nets in Base 32
(76, 76+27, 2640)-Net over F32 — Constructive and digital
Digital (76, 103, 2640)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 24, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (52, 79, 2520)-net over F32, using
- net defined by OOA [i] based on linear OOA(3279, 2520, F32, 27, 27) (dual of [(2520, 27), 67961, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3279, 32761, F32, 27) (dual of [32761, 32682, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3279, 32761, F32, 27) (dual of [32761, 32682, 28]-code), using
- net defined by OOA [i] based on linear OOA(3279, 2520, F32, 27, 27) (dual of [(2520, 27), 67961, 28]-NRT-code), using
- digital (11, 24, 120)-net over F32, using
(76, 76+27, 20167)-Net in Base 32 — Constructive
(76, 103, 20167)-net in base 32, using
- net defined by OOA [i] based on OOA(32103, 20167, S32, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(32103, 262172, S32, 27), using
- 1 times code embedding in larger space [i] based on OA(32102, 262171, S32, 27), using
- discarding parts of the base [i] based on linear OA(6485, 262171, F64, 27) (dual of [262171, 262086, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(19) [i] based on
- linear OA(6479, 262144, F64, 27) (dual of [262144, 262065, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(646, 27, F64, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- construction X applied to Ce(26) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(6485, 262171, F64, 27) (dual of [262171, 262086, 28]-code), using
- 1 times code embedding in larger space [i] based on OA(32102, 262171, S32, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(32103, 262172, S32, 27), using
(76, 76+27, 312363)-Net over F32 — Digital
Digital (76, 103, 312363)-net over F32, using
(76, 76+27, large)-Net in Base 32 — Upper bound on s
There is no (76, 103, large)-net in base 32, because
- 25 times m-reduction [i] would yield (76, 78, large)-net in base 32, but