Best Known (14−8, 14, s)-Nets in Base 128
(14−8, 14, 387)-Net over F128 — Constructive and digital
Digital (6, 14, 387)-net over F128, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 129)-net over F128, using
- digital (0, 4, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (0, 8, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
(14−8, 14, 460)-Net over F128 — Digital
Digital (6, 14, 460)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12814, 460, F128, 8) (dual of [460, 446, 9]-code), using
- 75 step Varšamov–Edel lengthening with (ri) = (1, 74 times 0) [i] based on linear OA(12813, 384, F128, 8) (dual of [384, 371, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(12813, 382, F128, 8) (dual of [382, 369, 9]-code), using an extension Ce(7) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12811, 382, F128, 7) (dual of [382, 371, 8]-code), using an extension Ce(6) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- 75 step Varšamov–Edel lengthening with (ri) = (1, 74 times 0) [i] based on linear OA(12813, 384, F128, 8) (dual of [384, 371, 9]-code), using
(14−8, 14, 513)-Net in Base 128 — Constructive
(6, 14, 513)-net in base 128, using
- net defined by OOA [i] based on OOA(12814, 513, S128, 12, 8), using
- OOA stacking with additional row [i] based on OOA(12814, 514, S128, 4, 8), using
- discarding parts of the base [i] based on linear OOA(25612, 514, F256, 4, 8) (dual of [(514, 4), 2044, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2564, 257, F256, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;1024,256) [i]
- linear OOA(2568, 257, F256, 4, 8) (dual of [(257, 4), 1020, 9]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;1020,256) [i]
- linear OOA(2564, 257, F256, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding parts of the base [i] based on linear OOA(25612, 514, F256, 4, 8) (dual of [(514, 4), 2044, 9]-NRT-code), using
- OOA stacking with additional row [i] based on OOA(12814, 514, S128, 4, 8), using
(14−8, 14, 413506)-Net in Base 128 — Upper bound on s
There is no (6, 14, 413507)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 316914 083492 743730 147050 651152 > 12814 [i]