MinT - Best Known (203−42, 203, s)-Nets in Base 4

Best Known (203−42, 203, s)-Nets in Base 4

(203−42, 203, 1060)-Net over F₄ — Constructive and digital

Digital (161, 203, 1060)-net over F₄, using

1 times m-reduction [i] based on digital (161, 204, 1060)-net over F₄, using
- trace code for nets [i] based on digital (8, 51, 265)-net over F₂₅₆, using
  - net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(203−42, 203, 5169)-Net over F₄ — Digital

Digital (161, 203, 5169)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−42, 203, 1911088)-Net in Base 4 — Upper bound on s

There is no (161, 203, 1911089)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 165 265702 044932 483165 841354 344350 465293 745088 780995 962486 224378 625372 121629 744613 095481 505360 168645 731846 492770 425395 807168 > 4²⁰³ [i]