Best Known (203, 203+37, s)-Nets in Base 4
(203, 203+37, 3657)-Net over F4 — Constructive and digital
Digital (203, 240, 3657)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 23, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (180, 217, 3640)-net over F4, using
- net defined by OOA [i] based on linear OOA(4217, 3640, F4, 37, 37) (dual of [(3640, 37), 134463, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(4217, 65521, F4, 37) (dual of [65521, 65304, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- discarding factors / shortening the dual code based on linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(4217, 65521, F4, 37) (dual of [65521, 65304, 38]-code), using
- net defined by OOA [i] based on linear OOA(4217, 3640, F4, 37, 37) (dual of [(3640, 37), 134463, 38]-NRT-code), using
- digital (5, 23, 17)-net over F4, using
(203, 203+37, 59862)-Net over F4 — Digital
Digital (203, 240, 59862)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4240, 59862, F4, 37) (dual of [59862, 59622, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4240, 65562, F4, 37) (dual of [65562, 65322, 38]-code), using
- (u, u+v)-construction [i] based on
- linear OA(423, 26, F4, 18) (dual of [26, 3, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(423, 27, F4, 18) (dual of [27, 4, 19]-code), using
- 1 times truncation [i] based on linear OA(424, 28, F4, 19) (dual of [28, 4, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(423, 27, F4, 18) (dual of [27, 4, 19]-code), using
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(423, 26, F4, 18) (dual of [26, 3, 19]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4240, 65562, F4, 37) (dual of [65562, 65322, 38]-code), using
(203, 203+37, large)-Net in Base 4 — Upper bound on s
There is no (203, 240, large)-net in base 4, because
- 35 times m-reduction [i] would yield (203, 205, large)-net in base 4, but