Best Known (29, 29+51, s)-Nets in Base 32
(29, 29+51, 120)-Net over F32 — Constructive and digital
Digital (29, 80, 120)-net over F32, using
- t-expansion [i] based on digital (11, 80, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(29, 29+51, 216)-Net in Base 32 — Constructive
(29, 80, 216)-net in base 32, using
- 4 times m-reduction [i] based on (29, 84, 216)-net in base 32, using
- base change [i] based on digital (5, 60, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 60, 216)-net over F128, using
(29, 29+51, 257)-Net over F32 — Digital
Digital (29, 80, 257)-net over F32, using
- t-expansion [i] based on digital (28, 80, 257)-net over F32, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
(29, 29+51, 258)-Net in Base 32
(29, 80, 258)-net in base 32, using
- 4 times m-reduction [i] based on (29, 84, 258)-net in base 32, using
- base change [i] based on digital (15, 70, 258)-net over F64, using
- net from sequence [i] based on digital (15, 257)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 15 and N(F) ≥ 258, using
- net from sequence [i] based on digital (15, 257)-sequence over F64, using
- base change [i] based on digital (15, 70, 258)-net over F64, using
(29, 29+51, 18717)-Net in Base 32 — Upper bound on s
There is no (29, 80, 18718)-net in base 32, because
- 1 times m-reduction [i] would yield (29, 79, 18718)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 80780 671630 918138 047963 052500 728224 431113 466739 095431 851219 822294 615888 386651 171405 932130 579208 954415 351029 927813 950665 > 3279 [i]