Best Known (121−21, 121, s)-Nets in Base 8
(121−21, 121, 26231)-Net over F8 — Constructive and digital
Digital (100, 121, 26231)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- digital (88, 109, 26214)-net over F8, using
- net defined by OOA [i] based on linear OOA(8109, 26214, F8, 21, 21) (dual of [(26214, 21), 550385, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8109, 262141, F8, 21) (dual of [262141, 262032, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8109, 262141, F8, 21) (dual of [262141, 262032, 22]-code), using
- net defined by OOA [i] based on linear OOA(8109, 26214, F8, 21, 21) (dual of [(26214, 21), 550385, 22]-NRT-code), using
- digital (2, 12, 17)-net over F8, using
(121−21, 121, 345076)-Net over F8 — Digital
Digital (100, 121, 345076)-net over F8, using
(121−21, 121, large)-Net in Base 8 — Upper bound on s
There is no (100, 121, large)-net in base 8, because
- 19 times m-reduction [i] would yield (100, 102, large)-net in base 8, but