Best Known (79−38, 79, s)-Nets in Base 25
(79−38, 79, 288)-Net over F25 — Constructive and digital
Digital (41, 79, 288)-net over F25, using
- net from sequence [i] based on digital (41, 287)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 41 and N(F) ≥ 288, using
(79−38, 79, 619)-Net over F25 — Digital
Digital (41, 79, 619)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2579, 619, F25, 38) (dual of [619, 540, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(2579, 648, F25, 38) (dual of [648, 569, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(29) [i] based on
- linear OA(2572, 625, F25, 38) (dual of [625, 553, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2556, 625, F25, 30) (dual of [625, 569, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(257, 23, F25, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- Reed–Solomon code RS(18,25) [i]
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- construction X applied to Ce(37) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(2579, 648, F25, 38) (dual of [648, 569, 39]-code), using
(79−38, 79, 214522)-Net in Base 25 — Upper bound on s
There is no (41, 79, 214523)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 273 715232 256063 795117 628731 966461 903458 120298 250860 312487 519721 597966 760117 169578 928823 059398 215547 751777 874585 > 2579 [i]