Best Known (70, 90, s)-Nets in Base 32
(70, 90, 104922)-Net over F32 — Constructive and digital
Digital (70, 90, 104922)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-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 (3, 13, 64)-net over F32, using
(70, 90, 209717)-Net in Base 32 — Constructive
(70, 90, 209717)-net in base 32, using
- 1 times m-reduction [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
(70, 90, 3447568)-Net over F32 — Digital
Digital (70, 90, 3447568)-net over F32, using
(70, 90, large)-Net in Base 32 — Upper bound on s
There is no (70, 90, large)-net in base 32, because
- 18 times m-reduction [i] would yield (70, 72, large)-net in base 32, but