Best Known (99, 99+25, s)-Nets in Base 8
(99, 99+25, 2759)-Net over F8 — Constructive and digital
Digital (99, 124, 2759)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 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 (82, 107, 2731)-net over F8, using
- net defined by OOA [i] based on linear OOA(8107, 2731, F8, 25, 25) (dual of [(2731, 25), 68168, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8107, 32773, F8, 25) (dual of [32773, 32666, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8107, 32774, F8, 25) (dual of [32774, 32667, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(81, 6, F8, 1) (dual of [6, 5, 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 Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8107, 32774, F8, 25) (dual of [32774, 32667, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8107, 32773, F8, 25) (dual of [32773, 32666, 26]-code), using
- net defined by OOA [i] based on linear OOA(8107, 2731, F8, 25, 25) (dual of [(2731, 25), 68168, 26]-NRT-code), using
- digital (5, 17, 28)-net over F8, using
(99, 99+25, 5461)-Net in Base 8 — Constructive
(99, 124, 5461)-net in base 8, using
- base change [i] based on digital (68, 93, 5461)-net over F16, using
- net defined by OOA [i] based on linear OOA(1693, 5461, F16, 25, 25) (dual of [(5461, 25), 136432, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(1693, 65533, F16, 25) (dual of [65533, 65440, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(1693, 65533, F16, 25) (dual of [65533, 65440, 26]-code), using
- net defined by OOA [i] based on linear OOA(1693, 5461, F16, 25, 25) (dual of [(5461, 25), 136432, 26]-NRT-code), using
(99, 99+25, 64910)-Net over F8 — Digital
Digital (99, 124, 64910)-net over F8, using
(99, 99+25, large)-Net in Base 8 — Upper bound on s
There is no (99, 124, large)-net in base 8, because
- 23 times m-reduction [i] would yield (99, 101, large)-net in base 8, but