Best Known (43, 43+22, s)-Nets in Base 64
(43, 43+22, 23831)-Net over F64 — Constructive and digital
Digital (43, 65, 23831)-net over F64, using
- 641 times duplication [i] based on digital (42, 64, 23831)-net over F64, using
- net defined by OOA [i] based on linear OOA(6464, 23831, F64, 22, 22) (dual of [(23831, 22), 524218, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6464, 262141, F64, 22) (dual of [262141, 262077, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6464, 262141, F64, 22) (dual of [262141, 262077, 23]-code), using
- net defined by OOA [i] based on linear OOA(6464, 23831, F64, 22, 22) (dual of [(23831, 22), 524218, 23]-NRT-code), using
(43, 43+22, 122675)-Net over F64 — Digital
Digital (43, 65, 122675)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6465, 122675, F64, 2, 22) (dual of [(122675, 2), 245285, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6465, 131075, F64, 2, 22) (dual of [(131075, 2), 262085, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6465, 262150, F64, 22) (dual of [262150, 262085, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6465, 262151, F64, 22) (dual of [262151, 262086, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(6465, 262151, F64, 22) (dual of [262151, 262086, 23]-code), using
- OOA 2-folding [i] based on linear OA(6465, 262150, F64, 22) (dual of [262150, 262085, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(6465, 131075, F64, 2, 22) (dual of [(131075, 2), 262085, 23]-NRT-code), using
(43, 43+22, large)-Net in Base 64 — Upper bound on s
There is no (43, 65, large)-net in base 64, because
- 20 times m-reduction [i] would yield (43, 45, large)-net in base 64, but