Best Known (97−22, 97, s)-Nets in Base 32
(97−22, 97, 95369)-Net over F32 — Constructive and digital
Digital (75, 97, 95369)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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 (63, 85, 95325)-net over F32, using
- net defined by OOA [i] based on linear OOA(3285, 95325, F32, 22, 22) (dual of [(95325, 22), 2097065, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3285, 1048575, F32, 22) (dual of [1048575, 1048490, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3285, 1048575, F32, 22) (dual of [1048575, 1048490, 23]-code), using
- net defined by OOA [i] based on linear OOA(3285, 95325, F32, 22, 22) (dual of [(95325, 22), 2097065, 23]-NRT-code), using
- digital (1, 12, 44)-net over F32, using
(97−22, 97, 190652)-Net in Base 32 — Constructive
(75, 97, 190652)-net in base 32, using
- net defined by OOA [i] based on OOA(3297, 190652, S32, 22, 22), using
- OA 11-folding and stacking [i] based on OA(3297, 2097172, S32, 22), using
- discarding factors based on OA(3297, 2097175, S32, 22), using
- discarding parts of the base [i] based on linear OA(12869, 2097175, F128, 22) (dual of [2097175, 2097106, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(12869, 2097175, F128, 22) (dual of [2097175, 2097106, 23]-code), using
- discarding factors based on OA(3297, 2097175, S32, 22), using
- OA 11-folding and stacking [i] based on OA(3297, 2097172, S32, 22), using
(97−22, 97, 2508951)-Net over F32 — Digital
Digital (75, 97, 2508951)-net over F32, using
(97−22, 97, large)-Net in Base 32 — Upper bound on s
There is no (75, 97, large)-net in base 32, because
- 20 times m-reduction [i] would yield (75, 77, large)-net in base 32, but