Best Known (62, 62+19, s)-Nets in Base 32
(62, 62+19, 116512)-Net over F32 — Constructive and digital
Digital (62, 81, 116512)-net over F32, using
- 322 times duplication [i] based on digital (60, 79, 116512)-net over F32, using
- net defined by OOA [i] based on linear OOA(3279, 116512, F32, 19, 19) (dual of [(116512, 19), 2213649, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3279, 1048609, F32, 19) (dual of [1048609, 1048530, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- 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(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(326, 33, F32, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
- extended Reed–Solomon code RSe(27,32) [i]
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- OOA 9-folding and stacking with additional row [i] based on linear OA(3279, 1048609, F32, 19) (dual of [1048609, 1048530, 20]-code), using
- net defined by OOA [i] based on linear OOA(3279, 116512, F32, 19, 19) (dual of [(116512, 19), 2213649, 20]-NRT-code), using
(62, 62+19, 233018)-Net in Base 32 — Constructive
(62, 81, 233018)-net in base 32, using
- 321 times duplication [i] based on (61, 80, 233018)-net in base 32, using
- net defined by OOA [i] based on OOA(3280, 233018, S32, 19, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(3280, 2097163, S32, 19), using
- discarding parts of the base [i] based on linear OA(12857, 2097163, F128, 19) (dual of [2097163, 2097106, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(12857, 2097163, F128, 19) (dual of [2097163, 2097106, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on OA(3280, 2097163, S32, 19), using
- net defined by OOA [i] based on OOA(3280, 233018, S32, 19, 19), using
(62, 62+19, 1445260)-Net over F32 — Digital
Digital (62, 81, 1445260)-net over F32, using
(62, 62+19, large)-Net in Base 32 — Upper bound on s
There is no (62, 81, large)-net in base 32, because
- 17 times m-reduction [i] would yield (62, 64, large)-net in base 32, but