MinT - Best Known (185−44, 185, s)-Nets in Base 4

Best Known (185−44, 185, s)-Nets in Base 4

(185−44, 185, 1036)-Net over F₄ — Constructive and digital

Digital (141, 185, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (140, 184, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 46, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(185−44, 185, 2212)-Net over F₄ — Digital

Digital (141, 185, 2212)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−44, 185, 348727)-Net in Base 4 — Upper bound on s

There is no (141, 185, 348728)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2404 914316 875551 623617 355152 140856 074172 811767 956538 447728 750619 831132 877991 390591 564037 716192 294819 780586 978433 > 4¹⁸⁵ [i]