Best Known (80, 110, s)-Nets in Base 32
(80, 110, 2282)-Net over F32 — Constructive and digital
Digital (80, 110, 2282)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 22, 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 (58, 88, 2184)-net over F32, using
- net defined by OOA [i] based on linear OOA(3288, 2184, F32, 30, 30) (dual of [(2184, 30), 65432, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3288, 32760, F32, 30) (dual of [32760, 32672, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3288, 32760, F32, 30) (dual of [32760, 32672, 31]-code), using
- net defined by OOA [i] based on linear OOA(3288, 2184, F32, 30, 30) (dual of [(2184, 30), 65432, 31]-NRT-code), using
- digital (7, 22, 98)-net over F32, using
(80, 110, 17477)-Net in Base 32 — Constructive
(80, 110, 17477)-net in base 32, using
- 322 times duplication [i] based on (78, 108, 17477)-net in base 32, using
- base change [i] based on digital (60, 90, 17477)-net over F64, using
- net defined by OOA [i] based on linear OOA(6490, 17477, F64, 30, 30) (dual of [(17477, 30), 524220, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(6490, 262155, F64, 30) (dual of [262155, 262065, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- linear OA(6488, 262144, F64, 30) (dual of [262144, 262056, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- OA 15-folding and stacking [i] based on linear OA(6490, 262155, F64, 30) (dual of [262155, 262065, 31]-code), using
- net defined by OOA [i] based on linear OOA(6490, 17477, F64, 30, 30) (dual of [(17477, 30), 524220, 31]-NRT-code), using
- base change [i] based on digital (60, 90, 17477)-net over F64, using
(80, 110, 192745)-Net over F32 — Digital
Digital (80, 110, 192745)-net over F32, using
(80, 110, large)-Net in Base 32 — Upper bound on s
There is no (80, 110, large)-net in base 32, because
- 28 times m-reduction [i] would yield (80, 82, large)-net in base 32, but