Best Known (62, 62+23, s)-Nets in Base 32
(62, 62+23, 3077)-Net over F32 — Constructive and digital
Digital (62, 85, 3077)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 18, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (44, 67, 2979)-net over F32, using
- net defined by OOA [i] based on linear OOA(3267, 2979, F32, 23, 23) (dual of [(2979, 23), 68450, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3267, 32770, F32, 23) (dual of [32770, 32703, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3267, 32771, F32, 23) (dual of [32771, 32704, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3264, 32768, F32, 22) (dual of [32768, 32704, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 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(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3267, 32771, F32, 23) (dual of [32771, 32704, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3267, 32770, F32, 23) (dual of [32770, 32703, 24]-code), using
- net defined by OOA [i] based on linear OOA(3267, 2979, F32, 23, 23) (dual of [(2979, 23), 68450, 24]-NRT-code), using
- digital (7, 18, 98)-net over F32, using
(62, 62+23, 23832)-Net in Base 32 — Constructive
(62, 85, 23832)-net in base 32, using
- 321 times duplication [i] based on (61, 84, 23832)-net in base 32, using
- base change [i] based on digital (47, 70, 23832)-net over F64, using
- 641 times duplication [i] based on digital (46, 69, 23832)-net over F64, using
- net defined by OOA [i] based on linear OOA(6469, 23832, F64, 23, 23) (dual of [(23832, 23), 548067, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6469, 262153, F64, 23) (dual of [262153, 262084, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(6469, 262155, F64, 23) (dual of [262155, 262086, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-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(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(6469, 262155, F64, 23) (dual of [262155, 262086, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6469, 262153, F64, 23) (dual of [262153, 262084, 24]-code), using
- net defined by OOA [i] based on linear OOA(6469, 23832, F64, 23, 23) (dual of [(23832, 23), 548067, 24]-NRT-code), using
- 641 times duplication [i] based on digital (46, 69, 23832)-net over F64, using
- base change [i] based on digital (47, 70, 23832)-net over F64, using
(62, 62+23, 190927)-Net over F32 — Digital
Digital (62, 85, 190927)-net over F32, using
(62, 62+23, large)-Net in Base 32 — Upper bound on s
There is no (62, 85, large)-net in base 32, because
- 21 times m-reduction [i] would yield (62, 64, large)-net in base 32, but