MinT - Best Known (252−59, 252, s)-Nets in Base 4

Best Known (252−59, 252, s)-Nets in Base 4

(252−59, 252, 1044)-Net over F₄ — Constructive and digital

Digital (193, 252, 1044)-net over F₄, using

trace code for nets [i] based on digital (4, 63, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(252−59, 252, 3119)-Net over F₄ — Digital

Digital (193, 252, 3119)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−59, 252, 632291)-Net in Base 4 — Upper bound on s

There is no (193, 252, 632292)-net in base 4, because

1 times m-reduction [i] would yield (193, 251, 632292)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 093684 944931 665319 947982 294537 628976 346760 060522 699312 961593 950884 760316 062947 789318 897130 788325 211572 570020 129226 471118 289396 393226 791249 669264 410008 > 4²⁵¹ [i]