Best Known (28, 28+50, s)-Nets in Base 32
(28, 28+50, 120)-Net over F32 — Constructive and digital
Digital (28, 78, 120)-net over F32, using
- t-expansion [i] based on digital (11, 78, 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
(28, 28+50, 216)-Net in Base 32 — Constructive
(28, 78, 216)-net in base 32, using
- 321 times duplication [i] based on (27, 77, 216)-net in base 32, using
- base change [i] based on digital (5, 55, 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, 55, 216)-net over F128, using
(28, 28+50, 257)-Net over F32 — Digital
Digital (28, 78, 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
(28, 28+50, 258)-Net in Base 32
(28, 78, 258)-net in base 32, using
- base change [i] based on digital (15, 65, 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
(28, 28+50, 16292)-Net in Base 32 — Upper bound on s
There is no (28, 78, 16293)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2523 203463 745719 370094 424417 800492 191259 514653 417064 175487 675022 669482 856794 692958 467819 720906 875709 353001 981053 755408 > 3278 [i]