MinT - Best Known (185, 185+51, s)-Nets in Base 4

Best Known (185, 185+51, s)-Nets in Base 4

(185, 185+51, 1060)-Net over F₄ — Constructive and digital

Digital (185, 236, 1060)-net over F₄, using

trace code for nets [i] based on digital (8, 59, 265)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(185, 185+51, 4536)-Net over F₄ — Digital

Digital (185, 236, 4536)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185, 185+51, 1548327)-Net in Base 4 — Upper bound on s

There is no (185, 236, 1548328)-net in base 4, because

1 times m-reduction [i] would yield (185, 235, 1548328)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3048 614160 292783 363921 570186 464717 794785 778134 996676 900457 468311 262022 769784 778587 393244 722435 355625 429512 210195 522192 295389 182709 875992 236468 > 4²³⁵ [i]