Best Known (92, 92+19, s)-Nets in Base 8
(92, 92+19, 58254)-Net over F8 — Constructive and digital
Digital (92, 111, 58254)-net over F8, using
- 81 times duplication [i] based on digital (91, 110, 58254)-net over F8, using
- net defined by OOA [i] based on linear OOA(8110, 58254, F8, 19, 19) (dual of [(58254, 19), 1106716, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8110, 524287, F8, 19) (dual of [524287, 524177, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8110, 524290, F8, 19) (dual of [524290, 524180, 20]-code), using
- trace code [i] based on linear OA(6455, 262145, F64, 19) (dual of [262145, 262090, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- trace code [i] based on linear OA(6455, 262145, F64, 19) (dual of [262145, 262090, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8110, 524290, F8, 19) (dual of [524290, 524180, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8110, 524287, F8, 19) (dual of [524287, 524177, 20]-code), using
- net defined by OOA [i] based on linear OOA(8110, 58254, F8, 19, 19) (dual of [(58254, 19), 1106716, 20]-NRT-code), using
(92, 92+19, 524296)-Net over F8 — Digital
Digital (92, 111, 524296)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8111, 524296, F8, 19) (dual of [524296, 524185, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8110, 524294, F8, 19) (dual of [524294, 524184, 20]-code), using
- trace code [i] based on linear OA(6455, 262147, F64, 19) (dual of [262147, 262092, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- 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(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(6455, 262147, F64, 19) (dual of [262147, 262092, 20]-code), using
- linear OA(8110, 524295, F8, 18) (dual of [524295, 524185, 19]-code), using Gilbert–Varšamov bound and bm = 8110 > Vbs−1(k−1) = 11 175336 576496 700365 290371 242454 314283 012677 675582 594754 438476 389156 054738 904322 563758 966076 899328 [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(8110, 524294, F8, 19) (dual of [524294, 524184, 20]-code), using
- construction X with Varšamov bound [i] based on
(92, 92+19, large)-Net in Base 8 — Upper bound on s
There is no (92, 111, large)-net in base 8, because
- 17 times m-reduction [i] would yield (92, 94, large)-net in base 8, but