Best Known (94−28, 94, s)-Nets in Base 5
(94−28, 94, 296)-Net over F5 — Constructive and digital
Digital (66, 94, 296)-net over F5, using
- trace code for nets [i] based on digital (19, 47, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
(94−28, 94, 755)-Net over F5 — Digital
Digital (66, 94, 755)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(594, 755, F5, 28) (dual of [755, 661, 29]-code), using
- 118 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 22 times 0, 1, 32 times 0, 1, 38 times 0) [i] based on linear OA(587, 630, F5, 28) (dual of [630, 543, 29]-code), using
- construction XX applied to C1 = C([623,25]), C2 = C([0,26]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([623,26]) [i] based on
- linear OA(585, 624, F5, 27) (dual of [624, 539, 28]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,25}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(583, 624, F5, 27) (dual of [624, 541, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(587, 624, F5, 28) (dual of [624, 537, 29]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,26}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(581, 624, F5, 26) (dual of [624, 543, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s (see above)
- construction XX applied to C1 = C([623,25]), C2 = C([0,26]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([623,26]) [i] based on
- 118 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 22 times 0, 1, 32 times 0, 1, 38 times 0) [i] based on linear OA(587, 630, F5, 28) (dual of [630, 543, 29]-code), using
(94−28, 94, 74545)-Net in Base 5 — Upper bound on s
There is no (66, 94, 74546)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 504879 668234 030814 376549 987672 696245 366366 064526 520494 007172 057985 > 594 [i]