MinT - Best Known (220−53, 220, s)-Nets in Base 4

Best Known (220−53, 220, s)-Nets in Base 4

(220−53, 220, 1036)-Net over F₄ — Constructive and digital

Digital (167, 220, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 55, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(220−53, 220, 2402)-Net over F₄ — Digital

Digital (167, 220, 2402)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−53, 220, 414330)-Net in Base 4 — Upper bound on s

There is no (167, 220, 414331)-net in base 4, because

1 times m-reduction [i] would yield (167, 219, 414331)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 709812 351023 572336 600811 426276 340753 949523 180414 568181 934134 669821 348696 783028 762878 387200 947473 831865 413209 325183 280578 906185 766487 > 4²¹⁹ [i]