MinT - Best Known (173−41, 173, s)-Nets in Base 4

Best Known (173−41, 173, s)-Nets in Base 4

(173−41, 173, 1036)-Net over F₄ — Constructive and digital

Digital (132, 173, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (131, 172, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 43, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(173−41, 173, 2131)-Net over F₄ — Digital

Digital (132, 173, 2131)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−41, 173, 416758)-Net in Base 4 — Upper bound on s

There is no (132, 173, 416759)-net in base 4, because

1 times m-reduction [i] would yield (132, 172, 416759)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 837454 078331 081861 440247 177507 236946 897945 118011 246819 479390 289278 839421 146446 653349 167210 424341 804109 > 4¹⁷² [i]