Best Known (77, 98, s)-Nets in Base 32
(77, 98, 104955)-Net over F32 — Constructive and digital
Digital (77, 98, 104955)-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 (60, 81, 104857)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 104857, F32, 21, 21) (dual of [(104857, 21), 2201916, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3281, 1048571, F32, 21) (dual of [1048571, 1048490, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3281, 1048571, F32, 21) (dual of [1048571, 1048490, 22]-code), using
- net defined by OOA [i] based on linear OOA(3281, 104857, F32, 21, 21) (dual of [(104857, 21), 2201916, 22]-NRT-code), using
- digital (7, 17, 98)-net over F32, using
(77, 98, 838860)-Net in Base 32 — Constructive
(77, 98, 838860)-net in base 32, using
- net defined by OOA [i] based on OOA(3298, 838860, S32, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3298, 8388601, S32, 21), using
- discarding factors based on OA(3298, large, S32, 21), using
- discarding parts of the base [i] based on linear OA(6481, large, F64, 21) (dual of [large, large−81, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(6481, large, F64, 21) (dual of [large, large−81, 22]-code), using
- discarding factors based on OA(3298, large, S32, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3298, 8388601, S32, 21), using
(77, 98, 6355945)-Net over F32 — Digital
Digital (77, 98, 6355945)-net over F32, using
(77, 98, large)-Net in Base 32 — Upper bound on s
There is no (77, 98, large)-net in base 32, because
- 19 times m-reduction [i] would yield (77, 79, large)-net in base 32, but