Best Known (93, 110, s)-Nets in Base 8
(93, 110, 262168)-Net over F8 — Constructive and digital
Digital (93, 110, 262168)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (82, 99, 262144)-net over F8, using
- net defined by OOA [i] based on linear OOA(899, 262144, F8, 17, 17) (dual of [(262144, 17), 4456349, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, 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(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using
- net defined by OOA [i] based on linear OOA(899, 262144, F8, 17, 17) (dual of [(262144, 17), 4456349, 18]-NRT-code), using
- digital (3, 11, 24)-net over F8, using
(93, 110, 2097206)-Net over F8 — Digital
Digital (93, 110, 2097206)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8110, 2097206, F8, 17) (dual of [2097206, 2097096, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8109, 2097204, F8, 17) (dual of [2097204, 2097095, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(8109, 2097205, F8, 16) (dual of [2097205, 2097096, 17]-code), using Gilbert–Varšamov bound and bm = 8109 > Vbs−1(k−1) = 242415 201163 136676 352822 865733 854377 170346 234986 048571 114220 298324 098363 444488 446943 445522 557636 [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(8109, 2097204, F8, 17) (dual of [2097204, 2097095, 18]-code), using
- construction X with Varšamov bound [i] based on
(93, 110, large)-Net in Base 8 — Upper bound on s
There is no (93, 110, large)-net in base 8, because
- 15 times m-reduction [i] would yield (93, 95, large)-net in base 8, but