Best Known (150−33, 150, s)-Nets in Base 8
(150−33, 150, 2050)-Net over F8 — Constructive and digital
Digital (117, 150, 2050)-net over F8, using
- 81 times duplication [i] based on digital (116, 149, 2050)-net over F8, using
- net defined by OOA [i] based on linear OOA(8149, 2050, F8, 33, 33) (dual of [(2050, 33), 67501, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8149, 32801, F8, 33) (dual of [32801, 32652, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8148, 32800, F8, 33) (dual of [32800, 32652, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 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(32) ⊂ Ce(26) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8148, 32800, F8, 33) (dual of [32800, 32652, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8149, 32801, F8, 33) (dual of [32801, 32652, 34]-code), using
- net defined by OOA [i] based on linear OOA(8149, 2050, F8, 33, 33) (dual of [(2050, 33), 67501, 34]-NRT-code), using
(150−33, 150, 32804)-Net over F8 — Digital
Digital (117, 150, 32804)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8150, 32804, F8, 33) (dual of [32804, 32654, 34]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8148, 32800, F8, 33) (dual of [32800, 32652, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 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(32) ⊂ Ce(26) [i] based on
- linear OA(8148, 32802, F8, 32) (dual of [32802, 32654, 33]-code), using Gilbert–Varšamov bound and bm = 8148 > Vbs−1(k−1) = 1 859589 710492 693005 243957 545341 176784 804174 610592 563732 815829 521810 906747 444870 555137 066090 994679 001009 695834 292998 081491 623254 886360 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 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(8148, 32800, F8, 33) (dual of [32800, 32652, 34]-code), using
- construction X with Varšamov bound [i] based on
(150−33, 150, large)-Net in Base 8 — Upper bound on s
There is no (117, 150, large)-net in base 8, because
- 31 times m-reduction [i] would yield (117, 119, large)-net in base 8, but