MinT - Best Known (113, 113+35, s)-Nets in Base 4

Best Known (113, 113+35, s)-Nets in Base 4

(113, 113+35, 1036)-Net over F₄ — Constructive and digital

Digital (113, 148, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 37, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(113, 113+35, 1901)-Net over F₄ — Digital

Digital (113, 148, 1901)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+35, 384464)-Net in Base 4 — Upper bound on s

There is no (113, 148, 384465)-net in base 4, because

1 times m-reduction [i] would yield (113, 147, 384465)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31828 855077 079755 475593 945480 353472 287862 269207 510884 724474 581108 589082 082009 913780 617300 > 4¹⁴⁷ [i]