Best Known (68, 88, s)-Nets in Base 32
(68, 88, 104902)-Net over F32 — Constructive and digital
Digital (68, 88, 104902)-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 (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 (1, 11, 44)-net over F32, using
(68, 88, 209717)-Net in Base 32 — Constructive
(68, 88, 209717)-net in base 32, using
- 321 times duplication [i] based on (67, 87, 209717)-net in base 32, using
- net defined by OOA [i] based on OOA(3287, 209717, S32, 20, 20), using
- OA 10-folding and stacking [i] based on OA(3287, 2097170, S32, 20), using
- discarding factors based on OA(3287, 2097171, S32, 20), using
- discarding parts of the base [i] based on linear OA(12862, 2097171, F128, 20) (dual of [2097171, 2097109, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(19) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(12862, 2097171, F128, 20) (dual of [2097171, 2097109, 21]-code), using
- discarding factors based on OA(3287, 2097171, S32, 20), using
- OA 10-folding and stacking [i] based on OA(3287, 2097170, S32, 20), using
- net defined by OOA [i] based on OOA(3287, 209717, S32, 20, 20), using
(68, 88, 2393737)-Net over F32 — Digital
Digital (68, 88, 2393737)-net over F32, using
(68, 88, large)-Net in Base 32 — Upper bound on s
There is no (68, 88, large)-net in base 32, because
- 18 times m-reduction [i] would yield (68, 70, large)-net in base 32, but