Best Known (90−20, 90, s)-Nets in Base 5
(90−20, 90, 400)-Net over F5 — Constructive and digital
Digital (70, 90, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 45, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
(90−20, 90, 4074)-Net over F5 — Digital
Digital (70, 90, 4074)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(590, 4074, F5, 20) (dual of [4074, 3984, 21]-code), using
- 939 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 11 times 0, 1, 25 times 0, 1, 54 times 0, 1, 104 times 0, 1, 175 times 0, 1, 249 times 0, 1, 307 times 0) [i] based on linear OA(580, 3125, F5, 20) (dual of [3125, 3045, 21]-code), using
- 1 times truncation [i] based on linear OA(581, 3126, F5, 21) (dual of [3126, 3045, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(581, 3126, F5, 21) (dual of [3126, 3045, 22]-code), using
- 939 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 11 times 0, 1, 25 times 0, 1, 54 times 0, 1, 104 times 0, 1, 175 times 0, 1, 249 times 0, 1, 307 times 0) [i] based on linear OA(580, 3125, F5, 20) (dual of [3125, 3045, 21]-code), using
(90−20, 90, 2211286)-Net in Base 5 — Upper bound on s
There is no (70, 90, 2211287)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 807 796106 713692 852219 464261 533730 858244 222641 299287 592403 742681 > 590 [i]