Best Known (66, 93, s)-Nets in Base 5
(66, 93, 296)-Net over F5 — Constructive and digital
Digital (66, 93, 296)-net over F5, using
- 1 times m-reduction [i] based on 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
- trace code for nets [i] based on digital (19, 47, 148)-net over F25, using
(66, 93, 848)-Net over F5 — Digital
Digital (66, 93, 848)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(593, 848, F5, 27) (dual of [848, 755, 28]-code), using
- 211 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0, 1, 31 times 0, 1, 39 times 0, 1, 44 times 0, 1, 48 times 0) [i] based on linear OA(583, 627, F5, 27) (dual of [627, 544, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(583, 625, F5, 27) (dual of [625, 542, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(581, 625, F5, 26) (dual of [625, 544, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- 211 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0, 1, 31 times 0, 1, 39 times 0, 1, 44 times 0, 1, 48 times 0) [i] based on linear OA(583, 627, F5, 27) (dual of [627, 544, 28]-code), using
(66, 93, 125276)-Net in Base 5 — Upper bound on s
There is no (66, 93, 125277)-net in base 5, because
- 1 times m-reduction [i] would yield (66, 92, 125277)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 20195 001712 705084 611186 474064 803774 602938 649472 453784 855324 011525 > 592 [i]