Best Known (94−20, 94, s)-Nets in Base 32
(94−20, 94, 104956)-Net over F32 — Constructive and digital
Digital (74, 94, 104956)-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 (57, 77, 104858)-net over F32, using
- net defined by OOA [i] based on linear OOA(3277, 104858, F32, 20, 20) (dual of [(104858, 20), 2097083, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3277, 1048580, F32, 20) (dual of [1048580, 1048503, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 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
- OA 10-folding and stacking [i] based on linear OA(3277, 1048580, F32, 20) (dual of [1048580, 1048503, 21]-code), using
- net defined by OOA [i] based on linear OOA(3277, 104858, F32, 20, 20) (dual of [(104858, 20), 2097083, 21]-NRT-code), using
- digital (7, 17, 98)-net over F32, using
(94−20, 94, 838860)-Net in Base 32 — Constructive
(74, 94, 838860)-net in base 32, using
- 321 times duplication [i] based on (73, 93, 838860)-net in base 32, using
- net defined by OOA [i] based on OOA(3293, 838860, S32, 20, 20), using
- OA 10-folding and stacking [i] based on OA(3293, 8388600, S32, 20), using
- discarding factors based on OA(3293, large, S32, 20), using
- discarding parts of the base [i] based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding parts of the base [i] based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- discarding factors based on OA(3293, large, S32, 20), using
- OA 10-folding and stacking [i] based on OA(3293, 8388600, S32, 20), using
- net defined by OOA [i] based on OOA(3293, 838860, S32, 20, 20), using
(94−20, 94, 7151314)-Net over F32 — Digital
Digital (74, 94, 7151314)-net over F32, using
(94−20, 94, large)-Net in Base 32 — Upper bound on s
There is no (74, 94, large)-net in base 32, because
- 18 times m-reduction [i] would yield (74, 76, large)-net in base 32, but