MinT - Best Known (256−63, 256, s)-Nets in Base 4

Best Known (256−63, 256, s)-Nets in Base 4

(256−63, 256, 1032)-Net over F₄ — Constructive and digital

Digital (193, 256, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 64, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(256−63, 256, 2473)-Net over F₄ — Digital

Digital (193, 256, 2473)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−63, 256, 370946)-Net in Base 4 — Upper bound on s

There is no (193, 256, 370947)-net in base 4, because

1 times m-reduction [i] would yield (193, 255, 370947)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3352 156415 374590 100731 717191 763909 640820 718997 091198 870976 305973 517154 834598 084620 779958 272192 371617 648146 882466 109701 410695 540375 165715 591400 177582 433280 > 4²⁵⁵ [i]