Best Known (37, 37+36, s)-Nets in Base 25
(37, 37+36, 230)-Net over F25 — Constructive and digital
Digital (37, 73, 230)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 27, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (10, 46, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (9, 27, 104)-net over F25, using
(37, 37+36, 499)-Net over F25 — Digital
Digital (37, 73, 499)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2573, 499, F25, 36) (dual of [499, 426, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2573, 642, F25, 36) (dual of [642, 569, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- linear OA(2568, 625, F25, 36) (dual of [625, 557, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [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(255, 17, F25, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(2573, 642, F25, 36) (dual of [642, 569, 37]-code), using
(37, 37+36, 146999)-Net in Base 25 — Upper bound on s
There is no (37, 73, 147000)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 1 121153 916163 967328 053102 540605 080930 372563 159585 677946 810744 273280 491482 601321 087779 267755 603516 681601 > 2573 [i]