Best Known (36−14, 36, s)-Nets in Base 32
(36−14, 36, 297)-Net over F32 — Constructive and digital
Digital (22, 36, 297)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 7, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 14, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 1, 33)-net over F32, using
(36−14, 36, 586)-Net in Base 32 — Constructive
(22, 36, 586)-net in base 32, using
- base change [i] based on digital (16, 30, 586)-net over F64, using
- 1 times m-reduction [i] based on digital (16, 31, 586)-net over F64, using
- net defined by OOA [i] based on linear OOA(6431, 586, F64, 15, 15) (dual of [(586, 15), 8759, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6431, 4103, F64, 15) (dual of [4103, 4072, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(6431, 4104, F64, 15) (dual of [4104, 4073, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(11) [i] based on
- linear OA(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-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(14) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(6431, 4104, F64, 15) (dual of [4104, 4073, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6431, 4103, F64, 15) (dual of [4103, 4072, 16]-code), using
- net defined by OOA [i] based on linear OOA(6431, 586, F64, 15, 15) (dual of [(586, 15), 8759, 16]-NRT-code), using
- 1 times m-reduction [i] based on digital (16, 31, 586)-net over F64, using
(36−14, 36, 2699)-Net over F32 — Digital
Digital (22, 36, 2699)-net over F32, using
(36−14, 36, 6002442)-Net in Base 32 — Upper bound on s
There is no (22, 36, 6002443)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1 532495 706945 582902 331547 521960 247837 479513 799461 410120 > 3236 [i]