Best Known (77, 96, s)-Nets in Base 8
(77, 96, 3670)-Net over F8 — Constructive and digital
Digital (77, 96, 3670)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 14, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (63, 82, 3642)-net over F8, using
- net defined by OOA [i] based on linear OOA(882, 3642, F8, 19, 19) (dual of [(3642, 19), 69116, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(882, 32779, F8, 19) (dual of [32779, 32697, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(882, 32780, F8, 19) (dual of [32780, 32698, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(881, 32769, F8, 19) (dual of [32769, 32688, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(882, 32780, F8, 19) (dual of [32780, 32698, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(882, 32779, F8, 19) (dual of [32779, 32697, 20]-code), using
- net defined by OOA [i] based on linear OOA(882, 3642, F8, 19, 19) (dual of [(3642, 19), 69116, 20]-NRT-code), using
- digital (5, 14, 28)-net over F8, using
(77, 96, 7283)-Net in Base 8 — Constructive
(77, 96, 7283)-net in base 8, using
- base change [i] based on digital (53, 72, 7283)-net over F16, using
- net defined by OOA [i] based on linear OOA(1672, 7283, F16, 19, 19) (dual of [(7283, 19), 138305, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1672, 65548, F16, 19) (dual of [65548, 65476, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(1672, 65551, F16, 19) (dual of [65551, 65479, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1657, 65536, F16, 15) (dual of [65536, 65479, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(163, 15, F16, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,16) or 15-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(1672, 65551, F16, 19) (dual of [65551, 65479, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1672, 65548, F16, 19) (dual of [65548, 65476, 20]-code), using
- net defined by OOA [i] based on linear OOA(1672, 7283, F16, 19, 19) (dual of [(7283, 19), 138305, 20]-NRT-code), using
(77, 96, 70724)-Net over F8 — Digital
Digital (77, 96, 70724)-net over F8, using
(77, 96, large)-Net in Base 8 — Upper bound on s
There is no (77, 96, large)-net in base 8, because
- 17 times m-reduction [i] would yield (77, 79, large)-net in base 8, but