Best Known (111, 111+22, s)-Nets in Base 8
(111, 111+22, 47664)-Net over F8 — Constructive and digital
Digital (111, 133, 47664)-net over F8, using
- 81 times duplication [i] based on digital (110, 132, 47664)-net over F8, using
- net defined by OOA [i] based on linear OOA(8132, 47664, F8, 22, 22) (dual of [(47664, 22), 1048476, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8132, 524304, F8, 22) (dual of [524304, 524172, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8132, 524310, F8, 22) (dual of [524310, 524178, 23]-code), using
- trace code [i] based on linear OA(6466, 262155, F64, 22) (dual of [262155, 262089, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [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(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(21) ⊂ Ce(18) [i] based on
- trace code [i] based on linear OA(6466, 262155, F64, 22) (dual of [262155, 262089, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8132, 524310, F8, 22) (dual of [524310, 524178, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8132, 524304, F8, 22) (dual of [524304, 524172, 23]-code), using
- net defined by OOA [i] based on linear OOA(8132, 47664, F8, 22, 22) (dual of [(47664, 22), 1048476, 23]-NRT-code), using
(111, 111+22, 650087)-Net over F8 — Digital
Digital (111, 133, 650087)-net over F8, using
(111, 111+22, large)-Net in Base 8 — Upper bound on s
There is no (111, 133, large)-net in base 8, because
- 20 times m-reduction [i] would yield (111, 113, large)-net in base 8, but