Best Known (107−24, 107, s)-Nets in Base 32
(107−24, 107, 87426)-Net over F32 — Constructive and digital
Digital (83, 107, 87426)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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 (70, 94, 87382)-net over F32, using
- net defined by OOA [i] based on linear OOA(3294, 87382, F32, 24, 24) (dual of [(87382, 24), 2097074, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3294, 1048584, F32, 24) (dual of [1048584, 1048490, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3294, 1048585, F32, 24) (dual of [1048585, 1048491, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3294, 1048585, F32, 24) (dual of [1048585, 1048491, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3294, 1048584, F32, 24) (dual of [1048584, 1048490, 25]-code), using
- net defined by OOA [i] based on linear OOA(3294, 87382, F32, 24, 24) (dual of [(87382, 24), 2097074, 25]-NRT-code), using
- digital (1, 13, 44)-net over F32, using
(107−24, 107, 174764)-Net in Base 32 — Constructive
(83, 107, 174764)-net in base 32, using
- 1 times m-reduction [i] based on (83, 108, 174764)-net in base 32, using
- net defined by OOA [i] based on OOA(32108, 174764, S32, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32108, 2097169, S32, 25), using
- discarding factors based on OA(32108, 2097171, S32, 25), using
- discarding parts of the base [i] based on linear OA(12877, 2097171, F128, 25) (dual of [2097171, 2097094, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(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(24) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(12877, 2097171, F128, 25) (dual of [2097171, 2097094, 26]-code), using
- discarding factors based on OA(32108, 2097171, S32, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(32108, 2097169, S32, 25), using
- net defined by OOA [i] based on OOA(32108, 174764, S32, 25, 25), using
(107−24, 107, 3057142)-Net over F32 — Digital
Digital (83, 107, 3057142)-net over F32, using
(107−24, 107, large)-Net in Base 32 — Upper bound on s
There is no (83, 107, large)-net in base 32, because
- 22 times m-reduction [i] would yield (83, 85, large)-net in base 32, but