Best Known (32, 32+30, s)-Nets in Base 25
(32, 32+30, 204)-Net over F25 — Constructive and digital
Digital (32, 62, 204)-net over F25, using
- t-expansion [i] based on digital (30, 62, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
(32, 32+30, 510)-Net over F25 — Digital
Digital (32, 62, 510)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2562, 510, F25, 30) (dual of [510, 448, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2562, 642, F25, 30) (dual of [642, 580, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- 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(2545, 625, F25, 23) (dual of [625, 580, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(256, 17, F25, 6) (dual of [17, 11, 7]-code or 17-arc in PG(5,25)), using
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- Reed–Solomon code RS(19,25) [i]
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2562, 642, F25, 30) (dual of [642, 580, 31]-code), using
(32, 32+30, 160578)-Net in Base 25 — Upper bound on s
There is no (32, 62, 160579)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 470 229176 544694 048140 036200 952740 033152 115282 154163 873363 032719 780600 072923 387090 185145 > 2562 [i]