Best Known (18, 28, s)-Nets in Base 64
(18, 28, 52429)-Net over F64 — Constructive and digital
Digital (18, 28, 52429)-net over F64, using
- net defined by OOA [i] based on linear OOA(6428, 52429, F64, 10, 10) (dual of [(52429, 10), 524262, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6428, 262145, F64, 10) (dual of [262145, 262117, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6428, 262147, F64, 10) (dual of [262147, 262119, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(6428, 262147, F64, 10) (dual of [262147, 262119, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6428, 262145, F64, 10) (dual of [262145, 262117, 11]-code), using
(18, 28, 131073)-Net over F64 — Digital
Digital (18, 28, 131073)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6428, 131073, F64, 2, 10) (dual of [(131073, 2), 262118, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6428, 262146, F64, 10) (dual of [262146, 262118, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6428, 262147, F64, 10) (dual of [262147, 262119, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(6428, 262147, F64, 10) (dual of [262147, 262119, 11]-code), using
- OOA 2-folding [i] based on linear OA(6428, 262146, F64, 10) (dual of [262146, 262118, 11]-code), using
(18, 28, large)-Net in Base 64 — Upper bound on s
There is no (18, 28, large)-net in base 64, because
- 8 times m-reduction [i] would yield (18, 20, large)-net in base 64, but