Best Known (48, 67, s)-Nets in Base 64
(48, 67, 29231)-Net over F64 — Constructive and digital
Digital (48, 67, 29231)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 12, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- digital (36, 55, 29127)-net over F64, using
- net defined by OOA [i] based on linear OOA(6455, 29127, F64, 19, 19) (dual of [(29127, 19), 553358, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using
- net defined by OOA [i] based on linear OOA(6455, 29127, F64, 19, 19) (dual of [(29127, 19), 553358, 20]-NRT-code), using
- digital (3, 12, 104)-net over F64, using
(48, 67, 233018)-Net in Base 64 — Constructive
(48, 67, 233018)-net in base 64, using
- net defined by OOA [i] based on OOA(6467, 233018, S64, 19, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(6467, 2097163, S64, 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(6467, 2097163, S64, 19), using
(48, 67, 633576)-Net over F64 — Digital
Digital (48, 67, 633576)-net over F64, using
(48, 67, large)-Net in Base 64 — Upper bound on s
There is no (48, 67, large)-net in base 64, because
- 17 times m-reduction [i] would yield (48, 50, large)-net in base 64, but