Best Known (121, 145, s)-Nets in Base 8
(121, 145, 43692)-Net over F8 — Constructive and digital
Digital (121, 145, 43692)-net over F8, using
- 81 times duplication [i] based on digital (120, 144, 43692)-net over F8, using
- net defined by OOA [i] based on linear OOA(8144, 43692, F8, 24, 24) (dual of [(43692, 24), 1048464, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8144, 524304, F8, 24) (dual of [524304, 524160, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8144, 524310, F8, 24) (dual of [524310, 524166, 25]-code), using
- trace code [i] based on linear OA(6472, 262155, F64, 24) (dual of [262155, 262083, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(6472, 262155, F64, 24) (dual of [262155, 262083, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8144, 524310, F8, 24) (dual of [524310, 524166, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8144, 524304, F8, 24) (dual of [524304, 524160, 25]-code), using
- net defined by OOA [i] based on linear OOA(8144, 43692, F8, 24, 24) (dual of [(43692, 24), 1048464, 25]-NRT-code), using
(121, 145, 664904)-Net over F8 — Digital
Digital (121, 145, 664904)-net over F8, using
(121, 145, large)-Net in Base 8 — Upper bound on s
There is no (121, 145, large)-net in base 8, because
- 22 times m-reduction [i] would yield (121, 123, large)-net in base 8, but