Best Known (153−28, 153, s)-Nets in Base 8
(153−28, 153, 18727)-Net over F8 — Constructive and digital
Digital (125, 153, 18727)-net over F8, using
- 81 times duplication [i] based on digital (124, 152, 18727)-net over F8, using
- net defined by OOA [i] based on linear OOA(8152, 18727, F8, 28, 28) (dual of [(18727, 28), 524204, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8152, 262178, F8, 28) (dual of [262178, 262026, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8152, 262181, F8, 28) (dual of [262181, 262029, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8152, 262181, F8, 28) (dual of [262181, 262029, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(8152, 262178, F8, 28) (dual of [262178, 262026, 29]-code), using
- net defined by OOA [i] based on linear OOA(8152, 18727, F8, 28, 28) (dual of [(18727, 28), 524204, 29]-NRT-code), using
(153−28, 153, 262183)-Net over F8 — Digital
Digital (125, 153, 262183)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8153, 262183, F8, 28) (dual of [262183, 262030, 29]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8152, 262181, F8, 28) (dual of [262181, 262029, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(8152, 262182, F8, 27) (dual of [262182, 262030, 28]-code), using Gilbert–Varšamov bound and bm = 8152 > Vbs−1(k−1) = 17783 998078 013307 336089 711947 672823 189771 301347 590693 547219 689180 943916 932097 517883 389638 080458 544498 261809 203766 275466 764215 201406 568136 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(8152, 262181, F8, 28) (dual of [262181, 262029, 29]-code), using
- construction X with Varšamov bound [i] based on
(153−28, 153, large)-Net in Base 8 — Upper bound on s
There is no (125, 153, large)-net in base 8, because
- 26 times m-reduction [i] would yield (125, 127, large)-net in base 8, but