Best Known (71, 71+21, s)-Nets in Base 32
(71, 71+21, 104901)-Net over F32 — Constructive and digital
Digital (71, 92, 104901)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 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 (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 (1, 11, 44)-net over F32, using
(71, 71+21, 209717)-Net in Base 32 — Constructive
(71, 92, 209717)-net in base 32, using
- 321 times duplication [i] based on (70, 91, 209717)-net in base 32, using
- base change [i] based on digital (44, 65, 209717)-net over F128, using
- net defined by OOA [i] based on linear OOA(12865, 209717, F128, 21, 21) (dual of [(209717, 21), 4403992, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12865, 2097171, F128, 21) (dual of [2097171, 2097106, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(12861, 2097152, F128, 21) (dual of [2097152, 2097091, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(12865, 2097171, F128, 21) (dual of [2097171, 2097106, 22]-code), using
- net defined by OOA [i] based on linear OOA(12865, 209717, F128, 21, 21) (dual of [(209717, 21), 4403992, 22]-NRT-code), using
- base change [i] based on digital (44, 65, 209717)-net over F128, using
(71, 71+21, 2247172)-Net over F32 — Digital
Digital (71, 92, 2247172)-net over F32, using
(71, 71+21, large)-Net in Base 32 — Upper bound on s
There is no (71, 92, large)-net in base 32, because
- 19 times m-reduction [i] would yield (71, 73, large)-net in base 32, but