Best Known (46−18, 46, s)-Nets in Base 64
(46−18, 46, 535)-Net over F64 — Constructive and digital
Digital (28, 46, 535)-net over F64, using
- 1 times m-reduction [i] based on digital (28, 47, 535)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (18, 37, 455)-net over F64, using
- net defined by OOA [i] based on linear OOA(6437, 455, F64, 19, 19) (dual of [(455, 19), 8608, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, 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(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using
- net defined by OOA [i] based on linear OOA(6437, 455, F64, 19, 19) (dual of [(455, 19), 8608, 20]-NRT-code), using
- digital (1, 10, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(46−18, 46, 1822)-Net in Base 64 — Constructive
(28, 46, 1822)-net in base 64, using
- net defined by OOA [i] based on OOA(6446, 1822, S64, 18, 18), using
- OA 9-folding and stacking [i] based on OA(6446, 16398, S64, 18), using
- discarding parts of the base [i] based on linear OA(12839, 16398, F128, 18) (dual of [16398, 16359, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1284, 14, F128, 4) (dual of [14, 10, 5]-code or 14-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(17) ⊂ Ce(12) [i] based on
- discarding parts of the base [i] based on linear OA(12839, 16398, F128, 18) (dual of [16398, 16359, 19]-code), using
- OA 9-folding and stacking [i] based on OA(6446, 16398, S64, 18), using
(46−18, 46, 8797)-Net over F64 — Digital
Digital (28, 46, 8797)-net over F64, using
(46−18, 46, large)-Net in Base 64 — Upper bound on s
There is no (28, 46, large)-net in base 64, because
- 16 times m-reduction [i] would yield (28, 30, large)-net in base 64, but