Best Known (76, 93, s)-Nets in Base 8
(76, 93, 32777)-Net over F8 — Constructive and digital
Digital (76, 93, 32777)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (68, 85, 32768)-net over F8, using
- net defined by OOA [i] based on linear OOA(885, 32768, F8, 17, 17) (dual of [(32768, 17), 556971, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- net defined by OOA [i] based on linear OOA(885, 32768, F8, 17, 17) (dual of [(32768, 17), 556971, 18]-NRT-code), using
- digital (0, 8, 9)-net over F8, using
(76, 93, 262183)-Net over F8 — Digital
Digital (76, 93, 262183)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(893, 262183, F8, 17) (dual of [262183, 262090, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(892, 262181, F8, 17) (dual of [262181, 262089, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(855, 262144, F8, 11) (dual of [262144, 262089, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(16) ⊂ Ce(10) [i] based on
- linear OA(892, 262182, F8, 16) (dual of [262182, 262090, 17]-code), using Gilbert–Varšamov bound and bm = 892 > Vbs−1(k−1) = 6899 519405 731815 121810 002424 852896 981810 474807 813467 758023 478124 438746 387049 333984 [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(892, 262181, F8, 17) (dual of [262181, 262089, 18]-code), using
- construction X with Varšamov bound [i] based on
(76, 93, large)-Net in Base 8 — Upper bound on s
There is no (76, 93, large)-net in base 8, because
- 15 times m-reduction [i] would yield (76, 78, large)-net in base 8, but