Best Known (167−28, 167, s)-Nets in Base 8
(167−28, 167, 37450)-Net over F8 — Constructive and digital
Digital (139, 167, 37450)-net over F8, using
- 81 times duplication [i] based on digital (138, 166, 37450)-net over F8, using
- net defined by OOA [i] based on linear OOA(8166, 37450, F8, 28, 28) (dual of [(37450, 28), 1048434, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8166, 524300, F8, 28) (dual of [524300, 524134, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 524302, F8, 28) (dual of [524302, 524136, 29]-code), using
- trace code [i] based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(27) ⊂ Ce(25) [i] based on
- trace code [i] based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 524302, F8, 28) (dual of [524302, 524136, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(8166, 524300, F8, 28) (dual of [524300, 524134, 29]-code), using
- net defined by OOA [i] based on linear OOA(8166, 37450, F8, 28, 28) (dual of [(37450, 28), 1048434, 29]-NRT-code), using
(167−28, 167, 601308)-Net over F8 — Digital
Digital (139, 167, 601308)-net over F8, using
(167−28, 167, large)-Net in Base 8 — Upper bound on s
There is no (139, 167, large)-net in base 8, because
- 26 times m-reduction [i] would yield (139, 141, large)-net in base 8, but