Best Known (39, 55, s)-Nets in Base 64
(39, 55, 32848)-Net over F64 — Constructive and digital
Digital (39, 55, 32848)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 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 (30, 46, 32768)-net over F64, using
- net defined by OOA [i] based on linear OOA(6446, 32768, F64, 16, 16) (dual of [(32768, 16), 524242, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using
- net defined by OOA [i] based on linear OOA(6446, 32768, F64, 16, 16) (dual of [(32768, 16), 524242, 17]-NRT-code), using
- digital (1, 9, 80)-net over F64, using
(39, 55, 262144)-Net in Base 64 — Constructive
(39, 55, 262144)-net in base 64, using
- 641 times duplication [i] based on (38, 54, 262144)-net in base 64, using
- net defined by OOA [i] based on OOA(6454, 262144, S64, 16, 16), using
- OA 8-folding and stacking [i] based on OA(6454, 2097152, S64, 16), using
- discarding factors based on OA(6454, 2097155, S64, 16), using
- discarding parts of the base [i] based on linear OA(12846, 2097155, F128, 16) (dual of [2097155, 2097109, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- 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(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(12846, 2097155, F128, 16) (dual of [2097155, 2097109, 17]-code), using
- discarding factors based on OA(6454, 2097155, S64, 16), using
- OA 8-folding and stacking [i] based on OA(6454, 2097152, S64, 16), using
- net defined by OOA [i] based on OOA(6454, 262144, S64, 16, 16), using
(39, 55, 427655)-Net over F64 — Digital
Digital (39, 55, 427655)-net over F64, using
(39, 55, large)-Net in Base 64 — Upper bound on s
There is no (39, 55, large)-net in base 64, because
- 14 times m-reduction [i] would yield (39, 41, large)-net in base 64, but